Yes, this is exactly the script I use.
"John would you like to choose game or position?"
[player says Paragon]
"John has chosen Paragon."
"Jane would you like to go 1st, 2nd, 3rd, or 4th on Paragon?"
[player says 4th]
"Jane chooses 4th. Jim would you like 1st, 2nd or 3rd on Paragon?"
[player says 2nd]
"Jim chooses 2nd."
Always be as explicit as humanly possible, and always give the players exactly the information they need to make a decision. This is the way I've always seen the PAPA staff do it, and if its good enough for them then its good enough for me.