You forgot to include a wetsuit on your gear list. I would put that in the #1 position on the list -- a wetsuit that fits and is of appropriate thickness for whatever water temp you'll be diving in. Some people have an unusual body type that doesn't fit into off-the-rack rental sizes. If this describes you, then make sure you buy your own wetsuit.
The more I dive, the pickier I've become with regard to the rest of my equipment.
I like the cracking pressure set to about 1" of water on my regs. If it's in the 1.5" range or higher, it just annoys me. Whether you rent or own regs you should be doing a comprehensive pre-dive inspection to ensure that the reg is functioning properly. I can't tell you how many times I've seen divers walk out of the LDS without first testing rental regs. It's crazy. Very few instructors teach their students how to do this.
I like my BCD to fit. My static weighting should promote good horizontal trim. With the vast majority of BCDs, these requirements can be met using the trim weight pockets and a couple of tank band pockets (I use the XS Scuba weight pockets mounted on the tank cambands). I can make conventional jacket-style BCDs, rear-inflate BCDs, and BP/Ws work for me. Whether you rent or own a BCD, please conduct a comprehensive pre-dive inspection. Once again, I've seen countless divers leave the dive shop without testing out the rental BCD. This is a HUGE oversight in my opinion.
Computers aren't fit-dependent. They are optional. One can very easily dive using tables, an analog depth gauge, and a dive watch. Computers are convenient, however. And they do help extend bottom time on a multi-level profile.
I'd probably buy gear in this order: wetsuit, BCD, reg, computer. The thinking behind my ordering is that the stuff that needs to fit should be purchased first. I have no qualms about renting BCDs or regs...but then again I do comprehensive checks on both pieces of gear to minimize chances of failure on a dive. I also have no issue with trying out 4 or 5 sets of rental regs to find one that works for me. Few people put that much effort into selecting rental gear.