I built my first "actual" computer all on my own and I have had no major problems. (a few hiccups here and there, but I got them solved). My old computers I had were "frankensein" computers, basically I mixed and matched. But its ALOT better to build your own. You'll save money and like Null said, you'll have a better understanding of each part.
Sites I would recommend for parts would be either
www.newegg.com or
www.pricewatch.com . I got most of my stuff from newegg.com since they have alot of great deals and whatnot.
What to order depends on what you want to keep from your current computer. If you just want to start all over on everything and go from the ground up, then let us know
It shouldn't be too hard to actually put everything together. It will probably take a few hours to put everything together, but thats obvious. And just to let ya know ahead of time, the first time you boot the computer after you put everything together, there is a good chance some kind of a problem will arise. But usually it should be easy to determine the problem. And if you have any problems setting it up, you can either shoot a reply/thread here or on a kind of fairly well known comp. forum site.