What type of drill bit should I use for pilot holes?
Drilling pilot holes is needed when the screws are large or it is on finished wood.
For example a #6 or #8 wood screw into a stud I probably would not drill a pilot into fur but oak studs that I have found in old Victorian era homes the screw would snap off if no pilot was drilled. The same is true with larger 1/4” lag bolts and screws, but I do start using pilot holes for studs at 1/4”.
To answer your question.
How do I size the pilot?
I hold the drill behind the screw and if I see the drill is wider than the body (not the threads) it is too large. I only want the pilot to take the amount out that is solid as this will reduce splitting. I do the same on finish work but wood screws the last 1/3 of the screw is not threaded. I want that pilot the size of the body where it is threaded.
This is a rule of thumb, sometimes on very soft wood a smaller drill is appropriate. Where the wood is hard like 100 year old oak, a larger bit will be needed. The last part is, if it is structural smaller is usually best but decorative larger again. This is to provide a pin without splitting.
I have been sizing wood screws like this since my dad taught me this over 50 years ago and it has served me well.