A few thoughts somewhat similar to the opinions above:
Here is what I did and why --
(1) Wetsuit/hood/gloves. I wear a XXXL wetsuit. These are often hard to find for rental. If you are a "standard-sized" person (whatever that is), this may not be as big of an issue.
(2) BCD & weightbelt -- as a newbie last year, the skill I was most worried about mastering was buoyancy. By fixing the main variables affecting my buoyancy (weighting system, wetsuit and BCD), I was able to master my buoyancy more quickly. As others have mentioned, fit is an issue as well. One final point here -- since we all attach various things to our BCDs (lights, octo/back-up reg, console, etc.), it is nice to have a standard config. Rental BCDs make it harder to streamline your gear since each one may have different/no D ring set-ups.
(3) Tank -- a few reasons here. I am a large human (and thus consume air at a faster than average rate) and wanted something bigger than an AL 80 to give me more bottom time. Also wanted a steel tank to help get some weight off of my belt/BC (again -- buoyancy).
(4) Regulator -- I felt like this was the piece of equipment I wanted to do the most research on. Regulators are easily rented, hose configurations are fairly similar and and sizing is generally not an issue. One counterpoint here -- I got sick a few times immediately after using rental regs. Can't prove that the reg was the cause...but something to think about.
(5) Computer -- this should be last because it is good to learn how tables work initially. This can be situational, however. If you are about to leave for a week-long liveaboard trip or a dive vacation where you are getting in 3-4 dives a day, a computer would be a must to maximize your diving $$$. If you are a newly certified diver and will be doing mainly shore diving in the near future at shallow depths, a computer is not as necessary. At shallow depths, you will be running out of air long before you hit NDLs, so this negates one big advantage a computer gives you (extended bottom times via continuous NDL computations based on varying depths during a dive).
As I said above, your "personal variables" (body type, future dive profiles, etc.) may cause you to change the order of purchase. Just think about the points I've made above and see how they apply to your situation.
Good luck!