I prefer not to use screwdrivers with insert bits - bits might get stuck in the screws and fall out. Wiha is my brand of choice.
I would recommend tweezers that would look like these -
http://www.techni-tool.com/758TW442 (any non-magnetic metal tweezers of that shape should work). These tweezers could be used to secure screws, small parts inside HDD and HSAs.
You would also need bigger tweezers for bigger parts(like clamps), they could be magnetic (ie cheaper). Preferably with serrations.
You might want to get two nose pliers - bigger ones for strong magnets and smaller ones when there is not enough space to use bigger ones. Any brand should work just fine, pick them by handle - should be comfortable with a good non-slip grip.