Can I have a 15 amp outlet on a 20 amp circuit with a 20 amp GFCI
This is legal and will work fine.  But you do need to use #12 wire because the circuit is protected by the 20 amp breaker. (you can add more if needed.)
I say this because the GFCI outlet is 1 device and the 15 A outlet is the 2nd.  If there were only a single 15 amp outlet, it would not be code.  But with 2 or more, it is ok.  NEC 210-21.b1