Allow me to add my voice to the chorus of people recommending #2 aluminum wire, and individual wires if the conduit run is complete end-to-end. (if it isn't, complete it).
I would avoid copper. The lugs on the subpanel will be aluminum because essentially all large lugs are (as well as neutral and ground buses). You don't want to deal with dissimilar metals.
Copper is not more deluxe, it's actually kind of a bad choice for feeder for above reasons.
Some people worry about aluminum because of stuff that happened in the 70s on small 15-20A branch circuits. That is poorly understood by the public, but in fact was not aluminum's fault; rather some comically bad misapplication of non-AL-rated receptacles, and failure to set torque to spec. Wrong torque continues to make problems for copper wire and torque drivers are now a Code requirement.
Aluminum has proven perfectly safe at these large sizes, and #2 is designed for 100A services but it can also be used for feeders up to 90A. The 60A breaker will accommodate #2 wire. It's very popular so it's unlikely to be out of stock.
#6 aluminum may also be available, that is good to 50A (so 2 banks of 50A each).
Assuming your conduit is continuous end to end, the cable types you can use are
- MH feeder for a cable with all conductors included in it
- THWN individual wires
- XHHW individual wires
- USE/RHW individual wires
- Cannot use SER or SEU as it is not rated for outdoors in conduit.
Make sure you are calling ALL stores in your area, not just Home Depot and Lowes. Include local family-owned lumber yards and electrical supply houses.
NM-B cable is not allowed outdoors, not even in conduit. UF cable is very flat and wide, and #6/3 UF requires 2" conduit as a result. All of these are hideously expensive compared to aluminum #2.
Paralleling two sets of copper wires is illegal. It requires the source end to be UL listed equipment specifically rated for paralleling.