What size drill bit would I use to drill hole to then to a 1/4" tap to make threads? Would I be using a 1/4 drill bit or is a 7/32" better since it is what I have and is undersized?

If you would get a 1/4″ tap to make threads, you would use #7 drill bit. Normally the tap should be 1/4″-20 UNC. It means there are 20 teeth within one inch long. So it is called UNC. If the tap is 1/4″-28 UNF. It means there are 28 teeth within one inch lone. So it is called UNF. But the tap 1/4″-20 UNC is normally used.