go to a place like Lowe's and they sell a really nice pack of twist bits for drilling holes - from 1/16th to 3/8" - and this comes in a tough little box which you can have forever.

For drilling bigger holes, I use a lot of "spade" bits - or "speed bores" - you can also get a bunch of different sizes of these at once. Then you can drill holes from 3/8" to 1 1/2".

Then for screwing in screws, go to a lumber store and get yourself a magnetic bit holder - it's a magnetic tip for your drill - and you can stick different screw driver bits into that - you can get Phillips or torque or square drive or traditional screw drives. The best brand I've seen is Apex - I use these things all the time since carpentry is my business.

One good place to get this stuff is a second hand store - sometimes there's piles of them, and you dig through and get a bunch of bits really cheap.

A good drill is something which will be handy for the rest of your life if you only use it from time to time.