Before a cup game or a qualifier, you should decide the order of your penalty takers. This can be done with a special orders form under the regular orders list.
Note that the first penalty taker is always the same as the one taking the set pieces during the regular game. If you change the first name on the special orders form for penalty shoot-outs, this is the same as changing the regular orders form on set pieces. The other 10 penalty takers can only be changed around by using the special orders form.
As for the order of the first 5 penalty takers, it isn't important. All teams start off with five penalties each, and if the game is still drawn after that, it'll proceed with sudden-death penalties – each team taking one penalty each until it's all been decided.
Like regular penalties, both the player's experience and his set pieces skill should be taken into consideration, but for a penalty shoot-out scoring skill and technical specialty are important too. The player least skilled at these abilities should be at the bottom of this list - penalty shoot-outs rarely go on beyond the first 10 penalties.