Any Ethernet cable can be used to connect to the wireless modem/router. They can be CAT5, or CAT6. CAT5s are cheaper, so get one of those. To test your internet speed you can go to Speakeasy - Speed Test
and test your speed.
Internet speed varies in different households, it depends on many factors.
- Quality of the phone line, older houses have generally older cabling.
- Distance between your house and the CO. This the phone company hub.
- Problems at your provider (this usually is corrected in few hours by the company)
Wifi problems are more likely to occur, do what as wand3r3r suggested.