Hey there Xeptra, here's my two cents.
If you're going for your first pieces of gear I would say get your mask, snorkel and fins. If you haven't already bought those they are essential.
Quick(ish) lowdown...
Mask - for a mask look for something that is good quality and sturdy construction. Don't go for Mares LiquidSkin bulls**t, and the like they are pretty (and extortionately expensive) but you're paying for average quality and gimmicks. Go for something like a TUSA Powerview - A great mask that fits loads of people easily, provides a great viewing angle and is sturdy, whilst still being relatively low volume. I was the first in my area to buy one of these (black is the way to go) and now I know about 15 people who I've converted. They're just a great mask, good price too.
Snorkel - don't waste a bunch of money. 15 bucks max, just make sure it has a decent mouthpiece and a purge valve at the bottom, splashguard is a bonus.
Fins - this depends on your legs, but a good idea is to go for Mares as they make great fins in a huge range. Try and stay away from split fins, they are terrible in currents and overpriced. Instead go for something open heel and with boots, but full blade, like TUSA Tri-ex or Maries Avantitre/Quattro/Superchannel. Helps to have a light colour for visibility underwater ie yellow/green. Going black black black makes you look cool, but looking cool doesn't mean jack.
Having covered that, the next thing I would buy would be your regulators: I agree with you on that. First off, you should try and avoid buying a regulator that is expensive to service and has lots of finicky parts and special tools needed to service them. Not naming names. Try to get yourself a set of apeks ATX40's or something similar, these regs are phenomenally simple in design and are tried and tested. Failing that, Scubapro is the next best thing.
As for a computer, that is a pretty difficult answer in short. It depends where you want to go withy your diving. If you're happy not switching gases yet and that sort of thing, something like a DiveRite Nitek Duo would be fine, its not pretty and full of gimmicky algorithms, it just does it's job.
I don't necessarily agree with mattboy on buying a BC and wetsuit first. You need to try a few to make sure which one is right for you, but i'd hardly say it would be the forerunner in purchasing your gear. As you're starting out, sometimes you may get a bit cold in the water, but a wetsuit isn't necessarily your life support system, whereas regulators are.
However, if I were to make a recomendation as to a good BC, it would be in favour of something like a Mares Pegasus MRS, which is rear inflation for good trim/balance in the water (if you're not teaching as an instructor it's the way to go), and it's NOT a backplate/wing setup which you really don't need to start with, as they are expensive, no matter how many dooders on here try to sell you one.
Not only that the Pegasus is cheap (249 on Leisurepro) and light and compact, so good for travel. Only downside is limited storage space ie. pockets.
If you need any advice, please don't hesitate to PM me.
-- Nemo