I'd like to get a desoldering station because those pumps DO let me down. I've gone through 3 of them by now. They're great when they're new. Then they start to get clogged, and then one day, right in the middle of heating up the board removing a chip or socket and bam, its stuck and wont budge. Screw that action jackson! I want the pro deal. Probably better off using the $3 hand pump thing versus the $20 one, that little pump ball wont fail.

I use the one from Princess Auto
http://www.princessauto.com/garage/welding/accy-s-components/3410022-vacuum-desoldering-tool
$7.99

I've used that braid a few times, most recently removing a coil.  It works ok, but it's a bit of a pain to get into odd places.  On a flat board it's fine, upside-down under a pf, not so much.

For a few extra bucks I keep a spare Teflon tip.. Usually they push out the old solder nicely. From watching the TOP videos I have learned how to use it properly.