This is one of those topics where ten people will recommend six products.
@DocMartin,
You will get differing opinions on this as well, but your best solution is to keep your PCs on at night. That is when all this housekeeping (backups and virus scans need to work anyway). I have always kept my PCs on, and as far as I know it hasn't caused my PCs to wear out sooner. In fact, some one say turning them off and turning them back on is harder on the drives and other moving parts.
But, if you must turn them off, I would check the settings in AVG. It is probably set to "If unable to run at a given time, run as soon as the PC is back on." I am not sure, but some AV programs have a setting where it turns off your PC anyway. You can also have your computer go into sleep mode at night. I bought this cool, very cheap meter that measures volts, amps and watts and I checked the different between the computers and/or the monitors being on, and there was hardly a difference.
Good luck either way. I use Trend Micro and love it, but AVG is an excellent program.