This request confuses me.

OP asks for inexpensive bicycle, but that is a quality bicycle, then notes that the bicycle will only be used once every few months for less than a 100 miles a year so it doesn't have to be a quality bicycle... and then there is talk about a primary commuter without it really being clear if this is a car, or a motorcycle or bicycle, and then some talk about strapping a full sized second bicycle to what possibly is a regular full sized primary bicycle?