I think this is 'basically' correct.
OEM - Can be used on one PC and is tied to the motherboard of that PC. License cannot be transfered to another PC.
Support comes from the manufacturer you purchased the PC from.
Retail - Can be used on one PC, but can be transfered to another PC as long as its no longer used on the old one.
Much more expensive than OEM. Comes with some support from Microsoft.
Your other question.
Yes, Vista Home basic is enough to play games and surf the intenet on.
It doesn't have the fancy Aero GUI, or media center etc, but thats a bonus in my personal opinion.

Its also by far the cheapest version.