Will your landlord allow installation of phone lines, cabling etc? I'm assuming not, otherwise the answer to your question is obviously "whatever is available in your area". Without any physical connection, your TV options are Saorview without an external aerial -- in many places it can be picked up with just an indoor antenna. Your broadband options are cellular and wireless. There is no such thing as "unlimited broadband", just the scandalous situation that providers can advertise a service as unlimited when it never actually is. Although the limits on some wired services might be high enough to get all your TV over internet, that's very unlikely on any cellular or wireless service.
A more general answer would depend on your area and what your landlord will/won't allow.