Homebrew PCBs

Generally you go by the size of the leads on the components. You want 
a drill that is about 5 to 10 percent larger. But at least a minimum 
of 0.002" to 0.004" larger in any case.

Specific sizes: Many components, including DIP packages, will be OK 
with a #65 - #72, or a 1/32" or a 0.8mm. Half Watt and larger 
resistors will need larger sizes. Capacitors are all over the map so 
a 3/64", #55 - #60, or a 1.2mm would be a good second size. Beyond 
that, you just have to measure your component leads. And do it BEFORE 
making the board unless you want to make it twice.

Carbide may not be the best choice for your first efforts. Carbide 
will break very easily so if you are using a hand drill or a drill 
press with any amount of play, you may snap the small diameter ones 
quickly. I would start with HSS (High Speed Steel) bits and work my 
way into carbide after some experience. A good HSS bit can last for 
many dozens, even hundreds of holes, even in fiberglass epoxy. And 
you can buy several HSS bits for the price of one carbide one.