I would second the general idea of buying first your mask, snorkel and fins (basic gear) and then what is not available for rent.
Normally the LDSs rent the minimum required gear, this is wetsuit, reg setup, BCD and tank (of course). You can have that for granted.
Then comes what you need to dive comfortable and geared for the dive , boot, gloves, hood, PDC, compass, knife, torches.
The gear available for rent, depending on the LDS, country, place, is, more or less, really used and abused.
For the time I've rented, I've found that wetsuits are teared , unsewed, unglued. BCDs that hardly keep the air in the bladders, broken pockets, inflator malfunctions, etc.
Regulators are taken with more care by the LDS, as a reg malfunction can cause a casualty.
Tanks are always taken with care, at least this is my experience.
So, for me, the order should be, and this is what I did :
1) Mask, fins and snorkel (needed for the OWD course)
2) Boots, gloves, knife and torch (main) (for night dives). Boots are required if you choose open heel fins.
3) Digital Camera and Water proof housing (if you like UW Photo).
4) Compass and PDC
5) BCD
6) Wetsuit and hooded vest
7) Reg setup
I have no plans to buy a tank, as there is no compressor facility near home, so, no use to buy one.