Rent all or most of your gear for at least 6 months. Most new divers don't continue with the sport/hobby. If you dive regularly for at least 6 months and still love it, then your're likely to become a long term diver. Rather than doing your OW and outlaying for something you may not continue with. After 6+ months you can then start buying gear. Usually buying a complete set is the cheaper option, where you can mix and match. During the previous 6 months of regular diving you should of had the oportunity to rent a good selection of gear and have researched different brands.
Keep in mind as well, that you should buy equipment that you intend to keep for 5-10 years, rather than buying entry level stuff with the aim to upgrade in a year or 3. It makes financial sense.
My wife and I are still using the same BC, regs and console we purchased 12 months after our OW, just before we did our AOW. The only upgrade/addition in 7 years has been a Suunto D6 and D4 in 2008 to compliment our Console computers. Our Cressi Titanium regs are still current and one of the easiest regs to breath even down at 40 metres. Glad we didn't cheap out on our reg purchase.
Your regulator set will be the most important piece of diving equipment you purchase. Have it serviced every 12 months and it will last A LONG TIME.
I agree that some renting can be good, especially if you can rent worthwhile gear. After that if a person has taken up diving and after a few dives feels in their gut that this is going to be a long term gig then they might as well make their best informed purchases and get on with it. By the time you dive regularly for at least 6 months you have more than paid for the gear in most markets. This assumes your words and my definition of diving regularly. Yes, it's great to make a 1st time lifetime purchase but that's not always realistic.
Nobody is married to their gear it can be sold at will for some percentage of the cost and you will still come out favorable to renting. If the diver never goes the distance there's a real good chance that they can still unload favorable to renting. Meanwhile they are in gear they know and trust.
The important thing is to do lots of homework. Be a gear forum junkie here on ScubaBoard and pay attention other forums too. After a while you'll know what matters, what to check and have a real good shot at making good buys. Using that approach my wife and I certified in our own gear and most of it stayed with us for hundreds of dives, some is still in active use.
When you think about it a regulator is a fairy objective purchase. They all work, spend what you can and get something you can have service, then breathe.
A wetsuit needs to fit and be warm enough. You can get plenty of guidance on thickness and here is
more than you need to know on the rest of it.
The computer can wait until you are content with your research. An SPG and beater watch are more than adequate for novice activity. The exception here is if you will making a dive intensive vacation in this period. (3+ dives a day for multiple consecutive days) In that case get a nitrox capable computer and take a nitrox class before going to get the most out of your vacation $$.
Fins can be subjective. Did you like the feel of what you used when you certified? Otherwise borrow or take a crap shoot. Magazine reviews an personal suggestions can help.
Weights... Get them in 5 pound and smaller increments so you can adjust down, avoid the bigger blocks.
Gloves, they just need to fit.
The BC is the one that trips many divers up. A nice simple tank BP&W rig is affordable and virtually takes fit risk out of the equation. If a jacket is preferred then buy where you can test dive preferably in open water or at least in a pool with your full wetsuit. If that is not possible bring a heavy sweatshirt to wear while trying BCs. Even if you completely mess this up a few dozen dives leaves you in a happy place. The 3 most important things of a BC are fit, fit and fit.
There may be some markets where renting is of real benefit. More often that not though rental gear is over the hill and not even of models you can buy. I suppose one other exception may be some vacation destinations. I have seen some of these where the gear is current and you can be in it for the length of your stay. In this case renting some portion of your needs can make sense.
Pete