I would first just drop the basic MySQL extension from the mix, as it does not support as many features as the newer extensions plus it is at best only in maintenance mode as far as development goes and is not enabled by default in PHP5+.
I don't know where AdoDB will fall into this, but my understanding is that the underlying driver is the same for MySQLi and PDO (or will be as of PHP 5.3.0). This article seems to indicate that initially MySQLi was faster than PDO, but in more recent releases the difference has disappeared -- I'm guessing due to the unification of using the same underlying driver now.
This article includes information on the functional differences between the MySQLi, PDO, and MySQL extensions.
Personally, I go with MySQLi if I only need to support MySQL on PHP5+, PDO if I need to be able to support MySQL plus other DBMS's, and MySQL if I need to support PHP4.