I would buy things in this order:
a). Dive computer (air integrated)
b). wet suit or dry suit (if you don't already have one)
c). BC
d). Regulator set (1st, 2nd, octo)
Nothing personal ND but I'm going to disagree with that.
The first on the list should be the 1st and 2nd stage/ octo setup. Spend all your money there. This is the piece of gear that your life depends on the most, is easily damaged and something you don't want to "rent". Did the person before you drag the octo through the mud and not clean it properly, does it tend to free flow or freeze up, is it tuned to breath too easy or hard? If you rent, each time out is a crap shoot. When you own it you know how it is treated, how it performs and when it was serviced last.
From there the order of computer, BCD, exposure suit is up to you. If you plan to travel/local dive a computer might be second. I'ts small so you will bring it on trips and in many places it is one thing you might not be able to rent. Like others have noted, leave the tanks for last. I would suggest a lot of hard thinking before impulse buying though. Your gear selection will depend on the type of diving you do. How often will you dive locally vs vacation, recreational vs technical etc...
A dry suit will set you back about $1000 or more retail and would be worth it if you plan to dive locally/year round. I hardly know anyone who dives the PNW year round in a wet suit. If not, renting a dry suit occasionally might be more cost effective. Just crunch the numbers on that one. Also, rent a few different brands/styles and see which you like. Also note the extras you might have to buy (rockboots, drygloves, undergarments).
About The computer. If you just plan to rec dive, a cheaper computer like a Suunto Gekko will do fine. It allows air/nitrox and gives all the pertinent info you need. From there you will pay more for extra features such as PC linking, AI etc... but you don't need that stuff if you don't want it. Depends on how much disposable income you have I guess.
Right out of the shoot I impulsively bought a jacket BCD which is ok for rec diving (I'll dive it for now) but in retrospect, I should have gone for a BP/W. I don't think it makes you a better diver or anything but the BP platform is the simplest, most reliable and allows for the most variation in gear configuration and adaptability down the road. All the splashy doo dads and sprinkles on most BCD's might look cool in the store but don't add to your experience in the water. On my BCD I have already removed the cummerbund, back pad and had to replace/add D rings to the proper location. I have quick release pockets but split my weight on a belt anyways and could just as easily put it all there.
I also think buying used is a good option. My reg set is X rental and came rebuilt with one free yearly servicing. Buying that way allowed me to get a quality rig for an affordable price. My LDS annually sells X rental Reg's, BCD's and dry suits. They replace their rental gear each year and use quality products so check some LDS's out in your neighborhood to see what's out there. New makes you feel good but once it's been dived a bit it's all used anyways.
Lastly, I can't stress how helpful a working relationship with an instructor/LDS owner (you can trust) can be. I spend a lot of time picking my instructor/owners brains about gear/configuration and he has talked me
out of buying a lot of useless gear.
