I have an Advent 7017, It's not the most powerful laptop by far but does run heat online perfectly ok with a wireless connection, the spec is below to give you some idea of what you need, as has been said you need to make sure that it has a good graphics card most laptops don't, so pay special attention to that.
CPU Intel Pentium 4 3.06 GHz (Northwood)
BIOS AMIBIOS. Press the Delete key to enter.
Memory 512 MB DDR SODIMM
Hard Drive 30 GB Hitachi DK23DA
CD Drive Slimtype COMBO LSC-24081
Screen 15" TFT (Native Res.1024x768)
Video Card ATI Mobility Radeon 9000 64MB DDR
Sound Card SiS 7012 audio chipset
Modem SmartLink 56K modem
Netword Card SiS 900 integrated fast ethernet