There are two ways to purchase scuba gear. The first is to get a package, either from your LDS or online. Packages typically save you some money when purchased all at once as compared to each individual piece bought separately. The benefit is obviously that is will save some money, especially when you continue to use your gear over time. The downside is that the package may include some items that the dealer has a hard time moving and will include that in the package with another more popular item. Some retailers will allow you to make your own gear selections in a package and give you a smaller discount. The other downside is that it requires a much larger cost up front. If you have a hard time affording just a BC or regulator you may not be able to buy both at the same time.
If you buy separately over time you then have smaller cost each time compared to a package. I usually recommend beginners look into purchasing what I call their personal fit items first such as wetsuit and BC. The most important recommendation for both of those items is that they fit you well, not their brand name. And, since every manufacturer varies in size and fit one brand may fit you well and one may not. That can be an issue when renting since most LDS and dive boats have only one brand that the carry. Nothing can ruin a dive like a poor fitting wetsuit or BC. Especially if you have a body type where the standard small, medium, and large doesn't always fit well. My daughter for example because of her age needed extra small sizes. Not every dive shop had XS small sizes and the small size often didn't fit well but was the only one available. She noticed on the first dive with her brand new BC we bought for her that fit well that her buoyancy was much better than when in rentals. After your personal fit items then I would purchase the computer and regulators. They are much less dependent of fit.
I would rush into buying any gear until after you officially certify and have an opportunity to try different types of gear. Personally I would recommend a back inflate BC over jacket style, but that is personal preference. Also, most entry level gear performs just as well as their more expensive counter parts but save quite a bit of money. They are also going to last a very long time so you should have them for years before they need to be replaced. You should do a lot of homework in looking into the gear you want to purchase and if possible even try it first before you buy. On the other hand, the cost of renting adds up and if you dive often enough an long enough you would be better buying sooner rather than later. With the amount of money I spent on rentals I would have been able to purchase a whole set of gear if I had taken the same amount of money off the bat and just bought the gear earlier.
Either way it depends on your financial situation and whatever works best for you.