It's hard to advise because there are so many choices, and preferences vary widely.
1.) Mask - I've tried a few, and for me, a $30 or so AquaLung SeaQuest Visage fits as well or better than any, including an Atomic mask I've got. But it might not work for you. If you know some other divers and have access to a pool or quarry, trying a few brand/models could save you money.
2.) Reg. - Atomic, ScubaPro, Apeks, AquaLung, all reputable. So are HOG. As mentioned above, a brand that a local dive shop will do routine servicing on locally is a plus.
3.) Octopus - one that breathes well costs more. If money is not tight, one that's the same brand as your primary reg. may be a simple choice.
4.) You may or may not want to talk about 'long hose' configuration, where for an OOA buddy you use the octo. & donate your primary. But this may complicate life more than you wish.
5.) Computers - console or wrist? Air-integrated or not? For console, I'd consider an Oceanic Pro Plus 3. If you've really got some money to spend, an Atomic Aquatics Cobalt 2 (be sure you get a 2, not a 1). For wrist units, there are many. The Oceanic VT4 air-integrated seems well-regarded. If you've got more money, the LiquiVision Lynx would offer you the option to find each other when diving with a like-equipped buddy. A lot of people love the Shearwater Petrel, but air-integration is not an option. I prefer computers with user-replaceable batteries, and a PC download kit that lets me download the computer's dive log to my computer, so I can max. depth, average depth, sac rate, nitrogen loading, total dive time, etc...without taking so many notes at the dive site.
6.) Fins - I like split fins, not everybody does. Whatever kind of fin you settle on, consider getting spring straps, which many people do agree on as a nice touch.
7.) Get a cutting tool (or 2) in case you get into some fishing line underwater; the Trilobyte is a fine choice that takes up very little space (I've got one in a pouch on my BCD webbing & you'd hardly know it's there). Jim Lapenta, mentioned above, sells them. For knives, I strongly prefer either Spyderco H-1 steel, or titanium steel, because regular stainless steel knives rust. The latter are not cheaper after a couple rust up on you. If you're not meticulous about post dive knife care, believe me now or later! 2 Cutting tools, located at different places on you, help make sure you can reach at least one. Some people like EMT shears.
8) BCD - this can be contentious. Jacket style are far & away most common in recreational diving. But you see BP&W advocated a lot on the forum, and especially for people into technical diving, where versatility lets divers use double tanks, etc... I haven't used a BP&W. If I were going to, I'd want someone like Lapenta to sell it to me and help me get the thing's webbing custom fitted. With BP/W, a steel back plate is heavier & lets you use less extra lead, but an aluminum back plate is lighter for air travel. Jacket BCD's, on the other hand, seem to be more 'off the rack.' I dive a Sherwood Avid and like it fine, but my experience isn't broad on these. If you want even more choices to confuse you, there are side-mount BCDs.
9.) Get an SMB and finger spool. This inflatable brightly colored tube will let the dive boat see you way easier if you surface a good bit from it, and help rescuers find you. Very nice backup to have with ocean diving.
10.) Find out if your local waters diving usually entails using a dive light, even on day dives. If so, you'll want a primary and perhaps a smaller, backup light.
Richard.