I started putting together my own gear fairly early in my limited dive career, and am happy about the decision. I think it's a good move, even if you want to spread out the purchases. My first purchase was a wrist PDC. Then I recently bought another PDC for much less $$ as a back-up and for my daughter. Read the thread about this one.
http://2sb.us/507564
If they are still available, it's a fantastic deal for $170 and it performed identically to my pricier PDC when I wore them both for some dives. It even has a decent digital compass. Main drawbacks to this $170 PDC: no USB cable for uploading data (I like uploading for logging and to review my dive profiles - I'm a bit OCD) and no option for air-integration (which is expensive, and lots of experienced folks dislike air integration anyway. I like it, but then I'm not experienced.)
Here's the direct link for the purchase:
https://www.divegearexpress.com/zeagle-n2ition-3-gas-dive-computer
I'd recommend putting in a fresh battery if you get one of these n2ition3 PDCs; mine was flakey at first, but has worked fine since investing the $5 in a new battery. Takes 30seconds and a highly specialized tool (a quarter aka 25cent piece) to change it.
->A possible issue with renting a computer is making sure you have the same unit for every dive during the entire trip (especially if you use more than one dive op.)
I think a regulator makes good sense as the next piece of personal equipment, and there seems to be a very sweet spot between the lowest end and the high end, especially if you look for last year's model after a change or consider buying used (and paying for immediate service.) And don't be afraid to mix and match for the octo and SPG to save $$. An SPG (with or without depth or compass) is close to indestructible compared to a reg, and retail prices can be obscene (IMO). Get a tight fitting cap, rinse your reg promptly, and you no longer have to worry about getting flesh-eating bacterial infections from rental regs. Plus it'll probably work better and you'll know your reg will perform consistently no matter where you travel. Buy a reg bag (I carry my Aqualung reg in $15 surplus Mares Reg bag. The reg doesn't seem to mind.)
BCD? BP/W? Yes, great to have, more expense, more to travel with, and much longer discussion. Glad I bought mine, YMMV.
Have fun!
-Don