An FM transmitter needs a VHF oscillator. Its frequency is varied by the modulation by using a varactor diode or by modulating the current of the oscillator transmitter which causes its capacitance to also be modulated whuch produces FM. For a transmitter whose frequency does not change all over the place then an RF amplifier is used as a buffer between the oscillator and the antenna.
Designing an FM radio receiver is difficult because parts are not available for FM radios anymore. Maybe you need to take apart an FM radio and use its parts in your design.