Also is 2-2-2-4 Mobile Home Feeder not available in your area? It may be cheaper than buying single THHN/THWN wire. The MHF is already assembled with a white marked neutral and a green ground where as the THHN/THWN you need to mark at the terminations.
Can you run MHF in the conduit? My understanding is that I can run MHF all the way from panel to panel and direct bury in the ground but that there is a risk associated with unprotected cable. I'm not too worried about digging animals but am concerned about some trees that are rooting where my trench is.

I must confess that at one time we owned a 28x40 on two acres - was a nice place. And damn cheap livin!
You have the correct wire. The HD web link you posted was not the wire you purchased.
It's 1:40AM, I'm going to bed. This has just tired me out.