Simple Linux upgrade script in Bash
The output of your script is lovely, but it strikes me as a work in progress.  There's nothing wrong with what is there, but it seems a few major pieces are missing.

error checking

What happens if one of the steps fails?  As it stands the script will diligently proceed to the next step.  If you actually checked the return codes from your apt commands you would also get a chance to use the RED color that seemed wasted in the comments above.

logging

You mention logging, but there is no such thing in the script.  Adding this would not be hard.  If you want your messages to go to the screen and a log you could add functions that log and write to the screen.  logger is handy way to add to the system logs, but you could write to your own $LOGFILE too with something like

echo "step $STEP: $MSG" &gt;&gt; $LOGFILE


docs

Shouldn't there be docs somewhere?  A link to a wiki page or something in the script would help folks figure out what is up.  Providing help from within the script if a -h is provided is a good habit to get into.

rewrite based on above

#!/bin/bash

RED="\033[1;31m"
GREEN="\033[1;32m"
NOCOLOR="\033[0m"

mylog() {
        STEP=$1
        MSG=$2

        echo -e "step $STEP: ${GREEN}${MSG}${NOCOLOR}"
        logger "step $STEP: $MSG"
}

myfail() {
        STEP=$1
        MSG=$2

        echo -e "step $STEP ERROR: ${RED}${MSG}${NOCOLOR}"
        logger "step $STEP ERROR: $MSG"
}

# handle command line options
if [[ $1 == "-h" ]]; then
        echo "usage: $0"
        echo " -h prints help"

        exit 1
fi

# step 1
mylog 1 "the start"
echo foo

# step 2
mylog 2 "a middle"
echo bar

# step 3
mylog 3 "the end"
echo baz
if [[ $? == 0 ]]; then
        myfail 3 "nothing really"
fi


finally

It is a good habit to run your scripts through shellcheck.net.  Even my short rewritten example has one thing that could be improved.