I know we are getting away from BC advice you asked for, but since it has come up, I have to give my 2 psi.
for me the gear in order of course is mask fins and a spare mask !!!!! and your own wetsuit or drysuit etc.. buy your own weight ? its cheap enough and you can set it up for you where you like etc..
then regulator setup with a good computer
then BCD
then tanks ?
Personnally, I'd get regs first (after the mask and fins that you probably had to buy before you could take your cert. class). Regs are the only pieces of gear that are truely life-support equipment (well, them and tanks, but see below on tanks), and I want to know how they've been handled, when they've been serviced, and by whom. Anything else I don't mind renting, but I'm paranoid about my regs. And if you do travel, go with Scubapro. Not that you'll die if you use any others
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but Scubapro, more-so than any other brand, you can get serviced everywhere should something go wrong with them. There's a lot of talk about which regs are the best, but for a given price point, among major brands, you would be really hard-pressed to tell any difference in performance. When I first got certified I bought a top-of-the-line Beuchat reg set. High test marks from major dive magazines. 'Best regs ever.' Then I moved and no one in the area serviced them... So I sold them and got some middle-of-the-line Scubapro regs. I can still breathe (can't tell any difference), and I can get them serviced anywhere I go.
BC would probably come next, just because rental ones suck. I can tolerate a sucky BC if I have to, though. As Honu alluded in his first post, if you have a variety of dive shops in your area, get in several dives with several different styles before you commit to buying. Try weight integrated versus belt, back inflate versus jacket style, etc. You may find out you disagree with my BC advice above. You have every right to be wrong.
Wetsuits aren't a priority for me. If you can don a commonly-available size, wetsuits can be rented easily enough. 'Course, you have to be comfortable with the idea that someone else has pee'd in it... Probably a lot of people.
Computer? If you trained on dive tables, the computer can probably wait. Plan your dive with the tables and use a watch. Computers give extra bottom time due to the fact that they do continuous calculations based on exact time at each depth, but until you get some experience and get comfortable in the water you'll probably be limited by air before NDLs. NOTE that I'm not saying don't watch your NDLs, I'm saying that the extended bottom time that a computer gives would not be utilized.
Lead? if you have diving available close-by, sure. If you are a vacation diver, and especially if you fly, rent. Most resorts actualy supply lead for free. Just keep a good log of how much you need for different conditions/configurations. However, if you go with a weight-integrated BC you'll have to make sure that the destination dive shop has soft weights available. Most weight-integrated BCs don't like bricks.
Tanks I can't justify buying. Maybe if I had a compressor and lived on a beach... Unfortunately, I don't. Tank rental around here is about $10. Tank fills are about $7. So if you own, you 'save' $3 per dive. It takes a lot of dives, at $3 per dive, to pay for a $150 tank. And that doesn't factor in the cost of annual visual inspections and hydro testing every, what is it, ten? years. Factor those in and owning a tank is never cost effective. I know that this seems to run counter to my regs argument above, but tanks and their associated valves are not likely to fail catastrophically during a dive. They're much more likely to fail before the dive ever starts. Just make sure you carry extra o-rings and inspect the ones on the tank valves before mounting your regs. Oh, and if you fly, and if the airline even allows tanks, you have to have the valve removed from the tank so it can be inspected. And anytime you have the valve off of the tank you're supposed to get it inspected by the dive shop...
I've never been worried enough to carry a spare mask, even though I use a prescription mask and am blind as a bat. I take care of my mask, and it is extremely unlikely to fail. Even if it were to fail, or get knocked off and I loose it, I feel confident I could get back to the surface just fine. However, if I did more dive travel I would probably get a spare, since I couldn't rent a prescription mask and I wouldn't want a lost mask to ruin an entire vacation.
Drysuits require additional training. Suggest you get a lot of dives under your belt, and really get your bouyancy nailed down, before you consider a drysuit. With a drysuit you have to manage the air in the suit in addition to the air in your BC. Matter of fact, I think drysuit cert requires advanced OW cert. Or at least a minumum numer of logged dives.