Avast works fine on WinME as far as i know, and as long as you allow avast to access the internet to update there will be no problems with sygate firewall with avast.
Also i would suggest that you install avast before sygate, as there possibly could be a problem/conflict if it is done the other way around, this is the same with ant Anti-virus and firewall product, but is not definate, only a possibility.
--lee