I would also try just a regular hammer drill vs. renting for such a small job.
Bit sizes: "The 3/16” tapcon uses a 5/32” bit, the 1/4” tapcon needs a 3/16” diameter bit, the 3/8” tapcon requires a 5/16”, the 1/2” tapcon requires a 7/16” bit, a 5/8”tapcon needs a 1/2” bit and the 3/4” tapcon...