I'm in the process of installing my wall connector now, & went with #6 THHN in PVC conduit, 60 amp breaker. My run was only about 30 ft with very few bends, so pulling the wire was relatively easy. I got the THHN at Lowe's. ($1.31/ft) Home Depot had it on their website, but the local store was out of it.
I overdid it, either out of extra caution or (more likely, ignorance), and used #6 for the ground wire as well. I could have used smaller, saved a few $$ and made the pulling easier, but it's done now.
I got a permit & having it inspected when I'm done, and hoping not to get nailed for some minor infraction, like the wrong type of conduit clamps, wrong conduit connectors, or whatever. Even if I need to re-do something, I'm still saving a ton of $$ compared to what an electrician would have cost. My total materials cost is less than $200.