Since you are going new you will have a hard time finding anything under 256MB ram. 512MB is probably about average now.
Processor size, pretty much anything offered now is going to be more then the average person would use. Anything over 2GHz should be fine. If I had the choice I would go with a P4 or AMD chip before a celeron. Celeron is Intels bottom of the line. A Celeron would likely work find for you.
Hard drive size - 80 gig or bigger is probably the standard now. 80 gig would be lots for most people unless you do a lot with videos.
Make sure it has NIC (Network card)
DVD writers are so cheap now you might as well get one. You can burn CDR's with them as well.
That's pretty much it unless you do a lot of gaming or somthing similar.
In my opinion you don't need to go with the latest and greatest computer any more. The sofware companies aren't keeping up and you will probably not use 1/10th of you computers capacity anyways.