For this particular command you can generally assume it'll work without errors most of the time. In this case, you may be better off just running it like this:
sudo apt-get update > ~/.aptget.update.log &
You can also hide all output using parenthesis:
(sudo apt-get update > ~/.aptget.update.log &)
This can be aliased with this line to make it handy you could use:
alias apt-update="(sudo apt-get update > ~/.aptget.update.log &)"
This lets you run the command using only 'apt-update'.
Put that in your ~/.bashrc
file to have it automatically run it each login.
You could also then add a custom message to remind you what it is doing:
alias apt-update="echo \"Running apt-get update in the background. Wait a few moments for it to finish.\" || (sudo apt-get update > ~/.aptget.update.log &)"