You dont say how much you want to spend, but a new laptop is going to cost you from �300 upwards.
You say you want it for internet and emailing, and you want it to be fast. To be honest, if all your are doing is interent and email then it does not need to be fast as you will mainly be limited by your broadband speed, not the speed of the laptop.
It will probably run Vista so you need 2Gb of memory.
Try to go for Vista Home Premium rather than Vista Home Basic.
Any laptop you buy nowadays will be wifi enabled so you can use it with your wifi router.
Try to get a good "name" make like Toshiba, HP, Dell, Sony, Fujitsu, Lenovo etc rather than the "badged" laptops from PC World like Advent, Packard Bell, or E Machines.
May be best to wait till after Xmas as their may be some bargains in the sales.