Redirect the stdout to /dev/null by appending > /dev/null to any command:
apt-get update > /dev/null
To also redirect stderr to /dev/null append 2>&1:
apt-get update > /dev/null 2>&1
To upgrade or install packages without being prompted for [Y/n] add -y:
apt-get upgrade -y > /dev/null 2>&1
apt-get install <package> -y > /dev/null 2>&1
You could also send it to a log file:
apt-get upgrade -y > script.log 2>&1
A single > will overwrite the file, to log multiple commands use two >>, which will cause the output to be appended to the end of the file:
apt-get update >> script.log 2>&1
apt-get upgrade -y >> script.log 2>&1