I went through the gear question myself when I certified a couple of months ago. I bought my regs and a computer first, closely followed by my BC and wetsuit. It's kind of hard to say which I would pick to buy first if I had to start over, but here's what I (personally) would take into consideration if I did it again:
Regs - What kind of diving will I be doing in the future? I purchased a reg that has some titanium parts in it, and now I'm looking into a Nitrox course in the fall - bad news, I have to either have the regs refitted or replace them for Nitrox diving. (Although I really like the regs, don't get me wrong
Computer - I would recommend a computer, even an inexpensive model as it will give you more bottom time and (I can imagine) takes a lot of load off of you while you are underwater. Bad news - I purchased a standard air computer and again Nitrox will force me to look into upgrading.
BC - I guess I lucked out and my LDS has a good set of BC's available, they were mostly newer model BC's. I could have gone a little while longer than I did before buying mine, but I'm impatient, so... You may want to check on the quality of your LDS's rental BC's - you may find that they are close enough to the model that you want to buy anyway so that you can start getting used to the general setup, and I've heard that some LDS's will apply part, if not all, of the amount of your rental towards the purchase of your BC in the future.
Wetsuit - Don't underestimate thermoclines and/or water's ability to cool you down
It can get rather chilly rather quickly down there - if you decide to dive without a wetsuit, don't hesitate to call the dive if you get too cold - keep in mind that it's your arse on the line.
The equipment that I'm going to replace for Nitrox diving will become my backup equipment / loaner equipment for a friend if one of them should decide to try diving, which is what I was (kinda) intending to do in the first place - buy one set of gear, replace it over time, and have a backup, but it's a more expensive proposition than it seems up front.
Again, this is my $.02 and I'm not sure what the board's exchange rate is running at right now, my advice may be worthless for your situation