mySQL overhead: Tweaking Scripts for Speed

I'm trying to figure out ways to tweak my scripts for performance. I've figured out that all mySQL queries should use indexed ids for speed. (For anyone who doesn't know: mySQL indexes fields with PRIMARY KEY, UNIQUE, or AUTO_INCREMENT in them. This means they're stored in binary trees internally, so access time is negligible for an INT PRIMARY KEY AUTO_INCREMENT). But how much overhead is there in: $link = mysql_connect($hostname,$username,$password) or die(""); $db = mysql_select_db($database,$link) or die(""); Would it be beneficial to run a single one at the beginning of every script? Currently I have a bunch of functions each with their own calls. Best Regards, Dan