IMO. Use MySQLi. It is the latest and greatest to date. I also recommend using the prepare statement any time you use the SELECT, INSERT, UPDATE, or DELETE statement.
$mysqli->prepare("SELECT bla, bla, bla FROM bla");
It does take a little more code to write, but is VERY secure when it comes to preventing sql injection attacks. Sql injection attacks are very common and are easily done by anyone who knows a little bit about PHP and SQL coding.