You can do anything you want if you got the cash.
Building a weapon is a good way to save some money though.
Burst, Auto Kits and other Class III items are exponentially more expensive and require you to either have a license to buy such items or purchase a tax stamp for each item you purchase. Tax stamps are typically $200, but can vary a bit depending on location.
If you are interested in building an AR rifle, there are many good sources of information here on TFL.
Some brands are not interchangeable with other brands. Uppers/Lowers are typically universal, but internal parts, such as trigger kits may not be. Bushmaster trigger kits are not compatible with Colt lowers for example. But you can strap a Bushmaster upper receiver on a Colt lower and vice-a-versa.
Best way to decide parts and specs is to decide how you are going to use it, how much you want to spend and begin questioning about brands and such considering those two things. You also want to consider where you live and any local laws regarding such a rifle. Magazine size, barrel length (typically must be minimum of 16"), etc... are things to think about.
Because they are designed to be from a high-count production line as well as to be disassembled in the field quickly for cleaning and replacing necessary parts, assembly of a military-style rifle of any kind is fairly simple and a person with a bit of will and patience should have no problems. There are hard-copy guides you can buy to help you along and teach you more than you probably need to know to put it together. There are also online guides available on some sites to take you through the process step-by-step.