C-band technology is emerging as an exciting innovative approach to the creation of compact new accelerators. Besides the possibility to sustain higher gradients and higher repetition rate operation at normal conducting temperature, it also allows one to increase the machine performance in terms of beam brightness. We propose the design study of a normal conducting, high gradient C-band injector aiming at the production of high brightness electron beams - up to 2.6×10³ TA/m² - at high repetition rate - up to 1 KHz - as desired to enhance the capabilities of modern radiation sources. This paper reports on beam dynamics studies that guided the injector design looking for a good compromise between the machine compactness and performances. For this purpose, a new standing wave C-band gun consisting of 2.6 cells has been designed to enhance the final beam brightness together with its own mode launcher to ensure the needed peak field at the cathode - up to 180 MV/m. Several working points in terms of peak current, transverse emittance and brightness are explored, showing the flexibility allowed by the proposed photoinjector. The integration of the gun mode launcher, that relies on a four-port configuration, in the injector design and its effect on the beam quality are also reported.