Simple. Monopole is the same as a vertical. Dipole you can receive 180 degrees on each side of the dipole, not very efficient for satellite work. I assume you are looking for something in the satellite area? If so then you will probably want to go with an omnidirectional antenna and not the Texas potato masher. Its matching section is too complecated for direct feed of normal coaxial cable. What you want is something that was introduced in 1972 which is the basic omni-loop antenna that can be found in the Radio Amateur´s Satellite Handbook from 1998 which is chalk full of information on this type of antenna. It is fully omnidirectional with one small 4 degree null because of phasing.
If needed I can send you the diagram for the antenna which uses common RG-58 cable and some wire.