Last year my kids and I built our first computer (https://pcpartpicker.com/b/xLNG3C), and it went so well, we decided to build another one. The kids are 11 and 9, now, and the new computer will be mostly used for my daughter's gaming (Skyrim, Rift, Minecraft with mods, and Trove are popular right now) and Photoshop digital painting (son gets last year's machine). We had a very strict budget, $700, and I plugged in our parts list here and fiddled, and waited to get the price we wanted. We already had a monitor, keyboard, mouse, and Windows--add all of those in and it's probably more like $1000.
The building itself went pretty well. We took our time and watched a lot of youtube videos anytime we got stuck, haha. We needed a micro-atx case to fit the spot in the desk where it would go (see the picture where it is snugged in, daughter likes the blue light, says it gives us "ambiance"). Thumbs up for final size, but the cable management was impossible--there is no space behind the mobo, you just have to try to get things twisted around under the drive bays. Still, it all worked when we turned it on (we cheered), and now that it is loaded up with software, the thing is zippy, beautiful graphics, and lag-free. Very happy!
Cable management aside (its ugly, I hang my head in shame) if you see any problems, let me know! I feel like we managed by the seat of our youtubing-pants. With noobs, it isn't the obvious things that throw you but the little details (silly small things like which side of the mounting bracket goes against the motherboard...that stopped us for ten minutes, or can 3 pin fans plug into 4 pin slots? apparently, yes).
Thanks go to pcpartpicker, we couldn't have done it without this site. Now each of the kids has a machine of their own, no more high level negotiations over whose turn it is, and they can play each other, super fun.