Firstly my advice would be NOT to buy from an auction site due to warranty unless your buying second hand. (not recommended)
You haven't stated what your budget is. As that will depend on the advice given. If your budget is per say 1000 then you have plenty to choose from. My advice is this: There is no such thing as a bad computer or laptop. What gives them a bad name is the after sales service, and the help desk..
So here are a couple of questions::
1. What is your budget?
2. Apart from what you have said above what exactly will you be using the laptop for?? i.e. Digital photography?? MP3 music?? Video?? get the idea
3. Will you be going Broadband?? or using the laptop on a home network i.e. linking the laptop to a PC at home??
Think very carefully of its potential use as then people can suggest video/graphics card,, sound card,, Memory,, hard drive capacity etc..