well, first always check your postings before actually posting them, a preview is a great tool.
Second, it depends on what you will be doing online. In fact, the most important thing for you will be internet bandwidth, not the computer itself. You will want something in the 10-30Mbps range (whatever is available in your area and fits in your budget).
For most classes an old Pentium 4 will do the trick if all you are doing is text and the occasional power point. But if you are doing constant power points, or other multimedia work then you will want a newer more modern computer, perhaps something in the Core2Duo to Core i3 range. An i3 is the most that you would ever need for school work unless you are doing full production work, and if that was the case then your school will provide the system specs required for your work. I would also suggest having 2-4GB of ram so that you can properly multi task.
The only other thing I would highly suggest is to have either a single large screen, or multiple monitors if your budget allows. When doing research it is handy to have multiple pages up, so the more screen real estate the better. I have a 27" monitor and have found it invaluable for large projects (and rather fun for games too).
Best of luck!