Should be good as gold to do that yourself.
The procedure I'd use is to first download the Avast home file
http://www.avast.com/eng/avast_4_home.html then the AVG removal tool
http://www.avg.com/download-tools (make sure you get the correct one for your OS, most likely 32 bit) -save both these files where you can find them -then
-disconnect from the net.
-Exit (or otherwise turn off/disable) the AVG
-Uninstall AVG from the control panel>add/remove programs
-reboot
-run the AVG removal tool, reboot if prompted
-Install Avast AV [edit, missed a bit] you'll be prompted to reboot during the process, and probably be prompted for a boot scan. Unless you are confident the computer is clean, allow the boot scan to run. It can take quite a while.
-reconnect to the net, check for updates.
A way to check is by right clicking the tray icon (blue ball, botoom right of the screen) select "updating", then "IAVS update" (which is the database.
Then you should be all good to go, provided ZA allows the processes. I've never used ZA, so I can't comment on how to set it, but the firewalls I have used usually prompt when a new process wants to connect. If that happens with Avast, click "allow" and "remember" or their ZA equivalents.
