Perhaps take a look at some of the netbooks?
ASUS 1000H, Samsung NC10, Dell Mini 9 or 12, Acer Aspire One: all good.
Wifi: it's just a radio signal. If you have a wireless router at home, you can use your own internet signal (at no extra cost to what you already pay for the internet).
If you're elsewhere, you need to find a hotspot. This is now nothing to do with your ISP at all. Some of these hotspots are free, some you pay for (at the counter at Starbucks or whatever).