First of all, $_POST is not a command, it's a variable, just like $choice is. That said, you should be able to do anything with $_POST['...'] as you can with $choice.
Second, 'choice1' is the index into the $_POST array. If you add <br> to that string, you're attempting to access a comletely different index. By index here, I mean that $_POST is a structure that allows you to associate a value with a name. The name of your values are 'choice1', 'choice2', and 'choice3'. There are no values named 'choice1<br>', which is why you get nothing.
echo $_POST['choice1'] . "<br>";
OR (as I prefer:)
For more info on variable substitution and string parsing, read the manual: