CareBear,
I'll probable repeat a few things that have already been said, but hopefully I can give another view.
First you have to see where you are at the present time. This includes a few things;
What are your feelings about diving? Do you like it, really like, love it, or are you still deciding?
What are your goals? Vacation diver or weekend (or more) diver?
What is your financial status? Can you afford to buy new, or will dive so often that you can't afford not to?
The benifits of renting is that it gives you time to determine if you like diving enough to spend the amount of money you will need in order to buy equipment. It also gives you the opportunity to try different types of equipment (makes and models). But, if you are diving regularly, those rental costs will amount to the level of buying your own equipment.
Owning your own equipment saves you rental fees and gives you the comfortable feeling of knowing the equipment your diving with, along with knowing the quality, the maint. that the equipment has had, etc. But of course, the price tag is steep.
My advise is to buy you equipment a little at a time. Buy your more personal items first and work from there. Also consider any special equipment that won't be easy to rent (example, odd size BCDs). Just use you head, don't be impulsive or rushed, research you equipment, and be an educated consumer so that you don't wind up with an expensive piece of equipment you won't, or can't use.
Good Luck and have a great vacation.
Bill