I have an eletrical AC unit with a 28.2 amp compressor and 3.1 amp fan. The nameplate on the unit specifies minimum circuit breaker size of 39 amps and maximum time-delay fuse of 60 amps. Two questions: 1) what size breaker do I need for this unit in breaker box? And 2) what gauge wire do I run from the unit to the breaker?

The breaker can be a 40 amp.

The wire size is based upon the circuit amps, which should be stated on the nameplate, some even tell you what min size wire is needed.

If you ran # 8 because that is the size wire for 40 amp circuit, you will be covered, however HVAC equipment can usually be wired with wire smaller than the overcurrent device, either fuses or CB.