bb,
The whole purpose of Avast is to protect you. It shouldn't be shut down when online.
However, you can remove it from the startup menu in MSCONFIG.
The On Line Protection providers (Standard/Outlook-Exchange/Internet Mail) can be shut down temporarily for the session by right clicking on the "a" icon in the tray and selection Stop On Acess and Exit.
Avast needs about 12mb for all its functions, but this really is not much. Users in the forum seem upset about it, but it was a trade off to have Avast run more stable, and give it better detection capabilities.
How much memory are you using? I would rather see you disable some other program/s than Avast.
Good Luck