Best practice to use $? in bash?

One common way is:

die() {
    IFS=' ' # make sure "$*" is joined with spaces

    # output the arguments if any on stderr:
    [ "$#" -eq 0 ] || printf '%s\n' "$*" 1>&2
    exit 1
}

then you use it like this:

mkdir -p some/path || die "mkdir failed with status $?"

Or if you want it to include the exit status, you could change it to:

die() {
    last_exit_status=$?
    IFS=' '
    printf '%s\n' "FATAL ERROR: $* (status $last_exit_status)" 1>&2
    exit 1
}

and then using it is a bit easier:

mkdir -p some/path || die "mkdir failed"

When it fails, mkdir will likely already have issued an error message, so that second one may be seen as redundant, and you could just do:

mkdir -p some/path || exit   # with the same (failing) exit status as mkdir's
mkdir -p some/path || exit 1 # with exit status 1 always

(or use the first variant of die above without argument)

Just in case you haven't seen command1 || command2 before, it runs command1, and if command1 fails, it runs command2.

So you can read it like "make the directory or die".

Your example would look like:

mkdir -p some/path || die "mkdir failed"
cd some/path || die "cd failed"
some_command || die "some_command failed"

Or you can align the dies further on the right so that the main code is more obvious.

mkdir -p some/path         || die "mkdir failed"
cd some/path               || die "cd failed"
some_command               || die "some_command failed"

Or on the following line when the command lines are long:

mkdir -p some/path ||
  die "mkdir failed"

cd some/path ||
  die "cd failed"

some_command ||
  die "some_command failed"

Also, if you are going to use the name some/path multiple times, store it in a variable so you don't have to keep typing it, and can easily change it if you need to. And when passing variable arguments to commands, make sure to use the -- option delimiter so that the argument is not taken as an option if it starts with -.

dir=some/path
mkdir -p -- "$dir"         || die "Cannot make $dir"
cd -P -- "$dir"            || die "Cannot cd to $dir"
some_command               || die "Cannot run some_command"

You could rewrite your code like this:

#!/bin/bash
function try {
    "$@"
    code=$?
    if [ $code -ne 0 ]
    then
        echo "$1 did not work: exit status $code"
        exit 1
    fi
}

try mkdir -p some/path
try cd some/path
try run_some_command

If you don't actually need to log the error code, but just whether the command succeeded or not, you can shorten try() further like so:

function try {
    if ! "$@"
    then
        echo "$1 did not work"
        exit 1
    fi
}

If you really want to exit on an error and are using Bash, then you should also consider set -e. From help set:

-e Exit immediately if a command exits with a non-zero status.

This of course doesn't give you the flexibility of a did_it_work() function, but it is an easy way to make sure your bash script stops on an error without adding lots of calls to your new function.