I bought one recently, 650-700 budget. Let's consider your options.
Try finding a prebuild computer with decent enough specs... Easier said than done. I looked at dell and ibuypower. Couldn't tell exactly what I was getting with a dell (you don't know what motherboard, psu you get right off the bat) and read some bad reviews of ibuypower. However, I may have been quite picky about it...
If you know how to build a computer, definitely go for it. Learning to do it can be a bit scary but so worth the experience. The parts I ordered had many diagrams for everything. Following pictures is pretty easy. Go to the new build forums of this website and people will help you out. Most likely, you'll get a much better price/performance. The forums are great for making sure your parts match up and you get the best deal. I would stick to this site for all your building needs. Newegg is a great site to scope out parts.
Just so you know, some people here have said budget computers are at least $1000... don't fret too much. If you can deal with lower resolutions and quality you can put together something decent for around $500. And $700-800 will get you quality parts and prepared for the future.
Research is the most time consuming of the whole buying a new computer process. You will probably start leaning towards building it yourself if you read enough. If you don't have the time, you are looking for a prebuild and are willing to accept any imperfections that come with it.