The design, construction and characterization of an atom chip apparatus for cold Rydberg atom experiments with 87Rb is presented. The apparatus is designed to investigate interactions between Rydberg atoms and the nearby chip surface, as well as the dynamics of Rydberg atoms in a double well. The proposed interrogation scheme is Rydberg electromagnetically induced transparency (Rydberg EIT). Magnetic trapping potentials used to load the chip with atoms are calculated. The atom number and temperature during various phases of the loading sequence are measured using absorption imaging. The room-temperature 4-level ladder-type Rydberg EIT system, in which the 3-level Rydberg EIT system is coupled via microwaves to a second Rydberg state, is investigated experimentally. EIT transmission spectra for different microwave powers and different polarizations of optical fields and microwaves are presented. It is shown that, to explain the observed polarization effects in the probe transmission lineshape, all magnetic sublevels, including the hyperfine structure of both Rydberg levels, have to be taken into account. The corresponding 52-level theory is discussed. Calculations of long-range multipolar Rydberg-atom Rydberg-atom interaction potentials are also presented and discussed.