The way you usually convert a &str to a String is to_owned, e.g.
"me".to_owned()
However, you can’t do pattern matching on a String. You could expect a success, get a &str from the String then pattern match on that:
fn player_starts() -> bool {
println!("Who will start (me/you)");
loop {
let input = readline::readline(">");
match input.expect("Failed to read line").as_ref() {
"me" => return true,
"you" => return false,
_ => println!("Enter me or you"),
}
}
}