Manogr,
You will get many opinions on this topic -- here's what I did and why:
(1) Mask, fins, snorkle, booties -- buy these ASAP. If you have to rent/borrow, it will be hard to ensure a good fit.
(2) Exposure suit -- I'm a large guy (XXXL wet suit) and it's hard to rent suits that fit me.
(3) BC/weight belt -- when you are a newbie, typically the hardest skill to master is your buoyancy. I wanted to "fix" the variables that affect my buoyancy ASAP when I was a brand new diver. Having your own BC/weights lets you get these variables configured the way you want them. Renting weight belts that you have to screw around with can be a pain. It's also important to be using a BC whose controls you are familiar with.
(4) Tank -- As a larger than average human, I use a lot of air. It's often hard to rent large tanks. This is one purchase that most folks would put last on the list. Gas capacity was important to me, though. Also, I bought an LP steel tank, which is -7.7 lbs buoyant when full and neutral when empty. This tank has much different buoyancy characteristics than an AL 80, which is normally neutral when full and positive when empty. It enabled me to get some weight off of my weight belt.
(5) Regulator/octo/SPG -- This was the piece of equipment that I was going to spend the most $$$ on and that I wanted to choose carefully. I tried many different regulators via rental, demo and borrowing -- Oceanic, Scubapro, Atomic, Mares before settling on an Apeks TX-100 with TX-40 back-up. I'm glad I waited and bought a reg set-up that will last me for a long time.
(6) Computer -- I think it is useful to use tables for at least a while to understand how they work. Computers are very important if you are going on a week-long vacation and getting in 20+ dives within a short period of time. If you are diving locally at shallow depths (where you will almost always run out of air before you hit NDLs), computers are not as important right away.
Again, this is what I did based on my own thought process and particular circumstances. Spend some time thinking about the diving you plan to do in the future -- rec, tec, cold, warm, vacations, etc. Also, talk to other divers here and elsewhere about what they bought and why. Finally, get some dives under your belt before buying too much gear. It's often hard to figure out what kind of gear works best for you without getting some experience in the water and exposure to what other divers are doing.
When you first start diving, you see the gear your instructor(s) uses and you assume it is a good configuration to emulate. As you gain more experience, you realize there are many choices with the types of gear you buy and how you set things up. It's better to realize this BEFORE you go out and buy everything, so you can make informed choices -- resulting in gear that works well for you and the types of diving you are doing now and in the future.
One other piece of advice -- sorry to be critical here, but this is my opinion. You are about to take an AOW class, where you will be on a deep dive. Be careful about using rental gear you are unfamiliar with in a situation where bad buoyancy control can lead to an accident.
Hope this helps -- good luck and dive safe!
