See here for explanation of standards: click here
Basically 802.11b has a max speed of 11 megabits per sec (mbps), 802.11g has a max speed of 54 mbps. The frequency is an integral part of the standard.
For most peoples' broadband purposes either is adequate. But, depending on the signal strength (due to intervening walls / distance) you may not get full strength at any given time.
I'd recommend getting an ADSL modem / router that supports 802.11b and g (most do - just check the specs).