Wireless G gives up to 54 Mbs. Ethernet can give up to 1Gbs. There are pro's and con's for each, and only you can decide what is the best fit for your needs:
With a wired system, you're restricted to be within the wire's length of the router. Alternatively you can wire you're entire house and have various Ethernet outlets around the house, but this'll cost a bit of money. You can get Gigabit Ethernet though, but this is only as good as the NIC's it is attached to. (e.g. You're not going to get Gigabit speeds on 10/100 cards.) You also get a bit more security, a plus if you transfer sensitive information.
Wireless. Less restricted by range, but a lower throughput than Ethernet. Speed degrades as signal strength decreases and distance from the router increases. So, if you're 60 ft. from the router and you're at 40% signal strength, you're certainly not going to get the full 54Mbs from wireless G. You have less security with wireless, but as long as you don't use WEP (use WPA or Radius instead) I wouldn't worry to much.