if you got a small site , then you should just buy a hosting package.
Otherwise start with VPS and then switch to dedicated (best to take a host that has decent VPS and dedi so you can easily switch when needed).
There are VPS hosts that go up to 1gb ram, 750gb transfer etc (about 80$)
jaguarpc for instance (sometimes they hand out 10%-15% discounts forever, so take a promo when its there). im retning the basic linux vps with them for about 17$