leah:
after mask, fins, and snorkel:
wet suit, because people pee in them
bc next because they all trim out and function differently
then reg and computer
as far as bc and reg, figure out what you want and then watch for a sweet deal--one will come. Before you buy the bc and reg figure out what you like and don't like from the rental gear first. Then you will make a better decision when you buy your own gear.
I agree with Leah but will add 1 thing...
If there is somehting that is difficult for you to rent than it goes to the top of the list. If are a not an off the rack suit person for whatever reason then buy something that fits even if it custom. If you are only comfortable in certain BCs then get the BC. For novice dives any regulator should suffice and you don't need a computer for a while.
All things being equal get your suit for the sake of hygiene and health. When the need is really there is is not healthy to hold back urine for an extended period. Given proper care this is no big deal but you can't count on that in a rental suit. Even if your interest fades you may get some use from a wetsuit for skin-diving, body surfing etc. Let's face it the sport has a high drop-out rate. Be practical and honest with yourself.
Next is your BCD. A little more costly and it's the core of the skills you are trying to master so lock it down.
Then comes you regulator set and analog instrument be they console/hose wrist or retactor mounted. The computer can come in here or as a final step. Actually I lied there is no final step but you get the drift.
Lights, reels, buoys, cylinders, more cylinders, pony bottle, drysuit, more fins, weight harness ............... Second set of gear for spouse, GF, or offspring :11:
Pete
PS a more complete profile is always helpful in making responses.