I also agree that the regulator should be your first purchase.  However, if you plan on buying a computer shortly, I think I would move the dive computer to the second purchase and then the BC third (as long as you can financially afford it).  Otherwise, you're going to either buy or rent a SPG to go with your regulator only to purchase a dive computer a short time thereafter.  While having the gauges as a back-up wouldn't be a bad thing, if you plan on diving a lot (as you indicated), you might as well put the money into completing the reg. package with the equipment you want.  Besides, I'd rather trust a rental wet suit or BC and rely on my own regulator and gauges.

A wetsuit should be your first purchase, it is a hygenic issue. No shop or resort adequetely disinfects wetsuits after use. Wetsuits are usually just rinsed off after being worn by other people who definetly will pee in the wetsuit and worse yet may have a skin or staph infection. The most versatile suit is a two piece 6mm wetsuit in that it is 2 suits for the price of one. You can wear just the jacket in a tropical environment and add the farmer john when itis cold.

The most important gear purchase is without question the regulator. Most rental regulators are not serviced or repaired until they break (I don't care what any body says about maintenance schedules), and you basically hope that the rental regulator doesn't break on your 80' dive. Buy a good one, you will own it for a long time. The regulator can fit in a regulator bag (Akona AKB604) and is small and easily transportable. The regulator is the foundation of safe and  comfortable diving. 

A computer is a very important gear purchase because most people don't plan their dive and dive their plan. Most divers just blindly follow an instructor or divemaster that they have known all of 20 min. at the dive resort. Most divers also forgot how or were never taught to use the repetative dive tables. Most computers are intuitively designed, easy to understand and extremely durable. They are easily transportable and properly used will facilitate safe diving.

If you are diving locally weight would be a good purchase. That way you can always have the proper configuration of weight on your belt or in your BC. If you only dive at resorts don't buy weights they are usually provided and you don't want to lug an extra 25# through the airport.

Don't buy a tank unless you have a high level of involvement in the sport locally or if you are technically training or leadership training. They are heavy to haul around, need maintenance, storage, and you can't fly with them. Tanks are easily and inexpensively rented. Most resorts provide them free.

If you are taking underwater photos you need a strobe. Lighting is the most important aspect to good underwater photos. If you don't have a strobe your photos will look green,gray and washed out (take a look at some of the photos in the photo gallery) Ikelite.com is a good place to start researching the best strobe for your photographic set up. Some underwater camera manufacturers have only specific lighting which can be used with their equipment, you must make sure everything is compatable.