Fir new divers I'd advise spluitting your gear into 4 roughly equal dollar valus groups.
First is the personal stuff, the stuff that has to fit and is in contact with your body and small stuff that is often not available in rental gear. You should get this about as soon as you certify OW. Even sooner for mask, fins snorkel.
That is:
Mask, its got to fit
Snorkel if you are going to use one, you put it in your mouth
Fins ( and boots) has to fit
Exposure suit has to fit and remember 85% of divers admit to peeing in a rental while 15% lie about it.
Weight belt, rental belts are notorious for having bad buckles or being overly long so it will fit anyone
DSMB, not often found in rental kits.
dive tool also not found in rental kits
Reg mouthpiece. I like the mold-able ones, much less jaw fatigue and easy to switch at the site
Next I am split between computer and reg set. I would suggest these as soon as funds allow. If you find a good deal on used or last of a model I would snap either one up as these can last a long time.
Computer so you have all dives logged from the start, while you can use paper logs and tables this is not very common any more.
Regs, you want to have one that you know will work one you control the maintenance history also the primary goes in your mouth
Finially I would advise the BC or BP&W set up. These are easy to rent and not a lot of difference on what is on the rental market with BCs.
I did not mention tanks, this will depend on where and how you dive, If you do resort diving then they always supply tanks, if you want to go self contained with just your buddies then you will need to but, depending on how often you dive it may be advantageous to just rent as you need annual inspection, 5 year hydro etc on these.
Somewhere along the line you will want to assemble a save a dive kit, underwater camera, drying and storage set up, underwater scooter, boat, compressor, tanks, SUV to haul the boat and gear, ocean front place so you can shore dive daily etc. Diving is a real good way to keep that bank balance from getting too high.