This depends on whether you want to store the command's output (either stdout, or stdout + stderr) or its exit status (0 to 255, with 0 typically meaning “success”).

To capture the output, you use command substitution:

output=$(command)      # stdout only; stderr remains uncaptured
output=$(command 2>&1) # both stdout and stderr will be captured

If you want both:

output=$(command)
status=$?

The assignment to output has no effect on command's exit status, which is still in $?.

If you want to capture stdout as well as taking action on success/failure, without explicitly storing or checking $?:

if output=$(command); then
    printf "it succeeded\n"
    ...