If you are just talking basics, a back plate (aluminum unless you will be for sure diving in very cold water with a dry suit and heavy undergarments, perhaps with a single tank), a one piece webbing (Hog) harness, with D rings on the left and right shoulder straps, left hip and at the rear of the 2" crotch stap a couple inches below the plate, and a non bungeed single bladder wing that is properly sized and suited for the tanks and the overall configuration, you will be hard pressed to find any instructor (GUE, TDI, NSS-CDS, NACD, NAUI, PADI whatever) who disagrees with the basic configuration for technical diving. It's very GUE/DIR, but before that it was very Hog and it works for basically everyone else as a starting point.
The differences individual instructors may suggest will be minor easy to fix things like a right hip D-ring, a scooter ring, or moving various D-rings up or down an inch or two. they will be things that are cheap to experiment with and if you don't like them, after the course, you can return to the basic configuration.
In short it is not all about a GUE/DIR/Hog configuration, but it is a configuration that is a pretty safe bet as a startign point with almost any instructor. Again, the only remotely difficult part is perhaps getting a wing that is well suited to the tank(s) you will be using and other considerations that impact the need for lift capacity such a stage and deco bottles, wehether you will be divign wet or dry, etc. So...you may want to check with your instructor before taking that partcicular leap.
I will say I do really like my Halcyon Explorer 55 lb wing and it is ideal with double LP 95's, stage and deco bottles, with enough lift, excellent trim and exceptional durability. But it is the only piece of gear you'll find I own with an "H" on it, as my plates are Dive Rite and OMS and my harnesses are pretty generic as are things like stage straps, etc. So don't let yourself get talked into an entire package.
SPG, etc:
A brass and glass SPG is standard (plastic ones are too easy to break). It is simple, relaible and idiot proof. The batteries will never die and there are no electronics to fail. A console is less than ideal as it adds a danglie and is a pita to unclip and veiw if you have to access it under stage or deco bottles. The SPG lives on the left hip d-ring for the most part and shares that space with the lower bolt snaps on any stage or deco bottles, so a console would just take up valuable space needed for other things and generally get in the way.
Get a bottom timer like the Uwatec bottom timer (pretty much a gold standard in tec diving) or get a cheap computer that also has a gauge mode (some, but not many entry level computers have this function. Alternatively, get a decent yet fairly inexpensive 2 gas nitrox computer (Uwatec Tec 2G, Tusa IQ-700/Dive Rite Duo, or Dive Rite Trio). You can then use it as a computer with nitrox and a deco gas, and/or use it in gauge mode on more advanced tri-mix dives.
Avoid the temptation for air integreation or even worse, wireless air integreation. Keep it simple, as simple = reliable = get you back alive with minimum drama. Drama = bad in technical diving (despite all the drama on The Deco Stop).
In any case, you need depth and time information as well as SPG info. As indicated above the SPG is on the hip and the depth/time information will be wrist mounted. Tobin at Deep See Supply makes exellent boots with bungee straps for the Uwatec bottom timer and tec 2 g as well as the Tusa IQ-700/Dive Rite Duo computer. And they are not expensive.
Regs:
If you are going tech assume you will eventually be diving doubles. also assume along hose (7') primary with a bungeed octo on a 22" to 24" hose with a brass and glass SPG clipped to the left hip D-ring. Good hose routing can be achieved with an L shaped reg first stage like the Scubapro Mk 25. A Scubapro Mk 10 is considered the baseline for flow rate, so the Mk 10, Mk 15, Mk 20 and Mk 25 all have more than enough (and I still see many Mk 5's in use on stage bottles and they will get the job done as well.
The other style is a diaphragm first stage with at least 1 Hp port and 2 LP ports on one side of the first stage. The Scubapro Mk 17 works very well as do most Apeks first stages, the Aqualung Legend, Poseiden first stages and Dive Rite first stages. (I personally tend to avoid posieden regs as they are finicky to adjust and techs who are good with them are few and far between in the US. Until recently they also used a higher than normal IP as well as an OPV integrated into the LP hose, limiting hose options and adding expense.) Round first stages with hoses poking out like spokes on a wheel (Aqualung Conshelf, Scubapro Mk 2, etc) don't work well due to really poor hose routing.
Get a high quality second stage and get a back up second stage that has an equal level of performance as you will donate the primary so in an OOA at depth, you will be the one using the backup reg - it needs to deliver the smae quality of breathing as the primary.
Reels:
The same thing applies with reels. Way back in the day I used a reef scuba reel that was state of the art at the time, but is now something I would not be caught dead using. The run of the mill dive rite reels falls in the same cataegory now and the really compex manta reels etc shoudl be avoided as well.
A good reel will have a means of maintaining a nice even drag on the line both with a set screw and with your hand and wil have a means to effectively lock the reel as well. Side handle reels rather than the older lantern handle style are becoming the reel of choice for most divers.
There are two styles of reels that most instuctors will not have an issue with:
1. The Larry Green/Ralph Hood design. It is a very open design on the assumption that a diver can and will birdnest a reel and it should consequently be easy to un tangle underwater without tools or dissassembling the reel. It is also very simple, very durable and has an excellent drag adjustment and lock screw and the open design also makes it easy for you to control the spool with your hand when running the reel. .
2. The Halcyon/Salvo design: This is a reel with very tight tolerances intended to prevent the line from every getting between the spool and frame. It is effective in that regard 99% of the time, but it tends to ignore the dictum that any attempt at idiot proofing is eventually defeated by the evolution of ever more capable idiots. If you end up in that 1% that can screw it up and you manage to bird nest it under water, you won't be able to fix it there. But the side handle design lets you easily wrap the line around the whole thing as you exit even it it is jammed (same with the Larry Green/Ralph Hood design).
A "primary" reel normally carries 250 to 400 ft. Most wreck or cave instructors will say you'll need one and your buddy will carry the back up for it. A priamary is used to provide a line from open water to the main line (which usually starts past the cavern zone ) in a cave, or from open water to where ever you penetrate in a wreck.
A "safety" reel is normally 150 ft. It is what it sasy it is, a reel you use in an emergency to find a lost line, etc. Reels work for this but it is more and more common to find people using a 150' finger spool. There are pros and cons either way and this is an area where instructors may have a definite and strong opinion.
"Gap" and "Jump" reels are used for...ummm...gaps and jumps. A gap is a break in the main line - usually across a sink or other opening in the overhead. A jump is what you put in to "jump" from one line to another to maintain a continuous guideline from the exit. Technically gap reels tend to have a bit more line than jump reels, maybe 75' versus 50', but the two are for all practical purposes interchangable. They normally look like smaller versions of primary reels and this is exactly the case with the Larry Green/Ralph Hood design. Finger spools are also commonly used in these applications.
Finger spools are obviously very useful (as a safety reel, a jump/gap reel, or to shoot a lift bag) and are virtually idiot proof as they are impossibel to jam. One or two 150' finger spools may be all you need for quite a while depending on the instructor and the type of class. The will work as safety reels or for shootig lift bags. Shorter 100' or 75' finger spools work great for jump/gap reels, but are too short to be used as a safety reel.
Line size varies a bit. #18 and #24 are smaller diameters that are common in cave diving where getting cut by sharp metal or abraded by loose/moving pieces of the wreck are not issues as you can get a lot more lenght on a given size reel or spool. #36 and #48, and to some extent 1/8", are more common in wreck diving as they are more resistant to cutting and abrasion. Braided nylon is the standard as nylon line sinks (floating line like polypropylene is an entanglement hazard) and braided line handles better underwater than twisted line - even though twisted line is slightly stronger.
Tanks:
What makes a tank ideal depends on whether you are diving singles or doubles, where you are diving, the rest of your configuration (exposure suit, wing, etc), and what the peopel you dive with are using. Having a set of double 130's won't do you any good if you have to gas match with buddies who all have double AL 80's as your penetration "third" will be 51 cu ft like theirs, not the 86 cu ft you actually have available. So again, hold on off tanks and manifolds until you know what's what and why you want or need a particular size tank in steel or aluminum. If you want to get extensive doubles experience prior to tech instruction, get an isoloator manifold using a two or three o-ring barrel design isolator crossbar (Sea Elite, Halcyon, Dive Rite, etc), use heavy duty stainless steel bands (with a reinforced center section) and either double AL 80's or X7-100's make good options. The AL80's can be used as stages later when you move to bigger tanks and both Al 80's and X7-100's are not overly negative so they help prevent over weighting. The 100s are very common and popular tanks and will be easy to sell if you later find you have the wrong tanks.
Fins:
No split fins. Ever. Period. Regardless of what any one else ever says or what any manufacturer claims. They suck with doubles and a dry suit. Scubapro Jet fins are hard to beat (but OMS beat them, as much as it pains me to say it). OMS Slipstreams are the same fin design but lighter, a bit stiffer and with better foot pocket proportions. Mares Plana Avantis and to a lesser extent Plana Quattros, are not bad. They are stiff enough to give you the horse power to get up to speed in doubles and they back kick ok.
Lights:
At some point you will need a can light. Things are changing fast, so don't spend big money for high end "death ray" technology as in a couple years you'll get the same thing for half as much money. The Dive Rite MR11 10 Watt HID is probaly the best deal around. It is a good little can light and works great in both caves and in poor viz on wrecks and it won't break the bank. Dive Rite will also upgrade the newer ones with black light heads to the LED 700 light head for $150, and the LED 700 is also an excellent light. Better in caves with decent viz in my opinion but does not burn through silty water quite as well the 10W HID.
Two back up lights is standard. LEDs are the way to go as they are more relaible than halogen lights and offer a lot more burn time. A halogen back up light was traditioanlly pretty dim as they had to be undervolted to ensure relaibility, so a modern LED is much brighter and the newer ones are pretty tightly focused. The Prinction Tec Torrent has excellent electronics, and I like every thing about it except the switch as it can tend to get turned on accidentally. But I still use them. Halcyon and Salvo make very good lights in terms of the bodies, but in my experience, they contract for the electronics with companies like Princeton Tec with the result that they end up selling electronics in them that are a generation or two behind the stuff you can get from the bigger name companies. And they tend to cost twice as much ($150 for a Scout or Rat compared to $70 for a Torrent that will be brighter). Keep it simple and again don't pay for bleeding edge technology as the field of bright white LED technology is advancing very rapidly.
No need to worry about a snorkle.