Neron,
I would recommend that you set Avast to automatically update the VPS and Program. This way, Avast will always be up to date. One of the best things about Avast is the Standard Shield which monitors your internet activity to PREVENT virus infection, and the Internet Mail module which scans email for you.
If you do not wish to be connected to the net, then Avast still monitors your computer, but the likely-hood of infection is minimal. Avast will then protect you from viri that HAVE ALREADY been stuck in your putter!
What exactly do you mean by "internet limited"....
Do you mean "time wise"?
or "bandwidth"?
Either way, Avast uses only what it needs.