What kind of semi-open file is better for your rook? What kind of semi-open file is better for your rook?

One where your pawn is on it, or one where the opponents pawn is on?
Generally when you read/hear something like "to put the rook on a semi-open file" it means a file where the opponent's pawn is on. The reasoning behind this is just piece activity, i.e. to maximize the available squares for the rook and also to attack something (the opponent's pawn on that file).

The only time where it makes sense (on general principles) to put a rook on a semi-open file where your own pawn is on, is if you want to support a passed pawn, typically with the rook from behind the pawn. However this situation would not be referred to as "putting the rook on a semi-open file".

PS: Of course there are situations (like the latter example above), where it could make sense to put the rook on a semi open file where your own pawn is located. However I understood your question as asking about the general principle that rooks are supposed to be good on semi-open files. In that  case it would always be the semi-open file with your opponent's pawn.