Guessing your hardware based on a Win 98 install, you could try Ubuntu, but, a lighter version of Linux designed for older computers, might be a better choice. Take a look at Xubuntu, and go from there (search for other alternatives).
http://www.xubuntu.org/
Though avast! for Windows won’t work on Linux, they offer an on-demand version for Linux. See details here:
http://www.avast.com/linux-home-edition