Building a lower is EASY, fun, and you gain more knowledge of how the rifle works. Uppers are more complicated and require more specialized tools (not many, but things like a torque wrench, vice, vice blocks, and lining up the gas port can lead to problems of not done right). A lot of people start by building their lower and strapping a completed upper to it.
IMO buying the parts and assembling saves you $$$, you get exactly what you want, and it's a fun time (until you lose your first takedown pin detent spring).
Buying name brand is good, especially of your buying their parts (do research, some name brands arent so hot) to build yourself. Look in to BCM if your budget allows, they are EXCELLENT. If you need to shave a few hundred off, look at Spikes Tactical or Palmetto State Armory. Both are also very high quality and they come with all the bells and whistles that the higher end comes with, but they batch test instead of individual test.
Buying premade incurs a more taxes and generally a higher markup than it would cost to buy a set of roll pin punches. Not recommended unless you has to question which end of the hammer you use.
If you are on a VERY strict budget and just HAVE to buy an AR15 now, then you can build complete rifles for sub-600 as well. Stay away from polymer lowers for the time being, they are still not as good as they should be and while the price is tempting, you are setting yourself up for failure if you go in to it expecting the rifle to perform like everyone elses. FWIW if you are in this category i can't suggest strongly enough that you wait and save up a bit and go with, at MINIMUM, PSA or Spikes. A PSA barebones rifle kit is really inexpensive and is a very large step up from rifles like the S&W Sport or a DPMS/Olympic Arms. Not saying those rifles won't work, not saying they are crap, I'm simply stating that for a LITTLE extra you can purchase from a manufacturer who has a reputation of putting out less "lemons" as well as get the features such as chrome lining and high pressure/magnetic particle inspection testing that you would otherwise miss out on.
Remember,
Buy cheap, buy twice.
A rifle is not something that you want to fail.