Its not hard, but if you really dont know what your doing it will be. If you have no idea, then i suggest buying one. Unless you have a friend that can help you out, two heads are better then one.
You can built a good computer with 1200$, also if you want a great monitor, i suggest a Viewsonic CRT. CRT monitors are big, but they are alot better then LCD and wont cost as much.
Like i said if you dont know what your doing, nor have a friend that can help you out. Then its not that good of a idea.
Heres a link to viewsonics website, take your time and look around they have some great monitors. You can order straight from ViewSonic, or click Buy Online, and find a better price at a different site. If you think you can handle builting a computer, then i will be more then happy to help you out.