Non UST tyres will work as well - they might drink a bit more sealant for the first few days as the sidewalls seal up. Use whatever tyres you like.

Here's a trick which you might find useful - when you first set up tubeless (particularly non UST) store the bike upside down sitting on the saddle and bars. That way if the tyres drop to (say) 5 psi then the bead won't come away from the rim where it would otherwise be squashed on the floor. The tyre will stay sealed - you can just top up the air quickly every time before you turn the bike right way up and ride. Eventually they'll seal completely and stop going flat.