Conversion times depend on how long your original avi is, and which converter you are using. Some encoders are slower---TMPGenc for example (good quality though). CCE Basic is a very good mpeg encoder, and one of the fastest, but is not the easiest to use for a beginner.
I normally use ProCoder2 and it takes me just under 3 hrs to encode a 350mb xvid file to mpeg2. I'm using an A64 2.2ghz with 2 gigs of ram, and always encode to a separate hard drive. A newer Intel processor would be a little faster.
If you want free options, look at SUPER or MediaCoder
The SUPER website is extremely annoying, but you will eventually get to a download page.