I wouldn't complicate things. If you have screw terminal available use it. As long as it is rated for the awg (size) of wire you are working with you will be fine.
I'm personally in favor of twist locks in all my equipment. I've seen tons of range and dryer plugs and recepts fail over the years. I've only seen a couple twistlocks burn up. Typically range and dryer plugs get plugged in and stay there for years so they work fine for that type of use. If...
I would just keep it simple. Install a gfci breaker in the panel on the new circuit that feeds your controller. Then run 10/2 romex to a L6-30r receptacle.
If you plan on running a 50a brew panel ever I strongly suggest running a minimum 60a sub feed circuit it the garage. Otherwise if you're going with the standard 30a set up you will only need 10awg wire to your control box. You see often people using dryer or range receptacles, a lot of times...
Sub panel is only required to have grounding electrode (rod, plate, pipe... Depends on what is accepted where you live based on the soil) if it is a detached building.
"Grounded conductor, grounding conductor, Grounding electrode / grounding electrode conductor. Learn the difference / understand the difference between these. Will help you tons before too lost
The quad breaker that somebody else suggested is probably your best bet if you plan on running a sub panel, just know that the tandem or quad breakers are engineered only to fit on the bottom five spaces on either side of the panel. You could also run the surge protector in parallel off...