Hey Daniel,
I'm just going to go down the list, and if I mention something you already knew about, I apologize in advance for that! Here goes!
The angle of the slots on a METRIC Phillips Screw is different than on an American Phillips Screw. So if you're trying to get a metric screw out with that crusty old Craftsman Screwdriver, then that's not gonna' work!
I'm a BIG Fan of using "Nut Buster" or "Liquid Wrench" on any fasteners I am trying to remove from my bikes.
Lastly, I have attached a pic of a "Must Have" Tool when working on ANY bike, and that is a Impact Driver. The one in the pic is a bit "Fancy" but Harbor Freight sells one for less than $20. that does the job just fine. It's better to start out using the Impact Driver than to destroy the screw head and try to remove it after the fact.
I hope this helps,
Earl.