Re: Wait for the turn for more equity or not?
Calls. Check-raising here will do absolutely nothing except build the pot, and your equity edge is not all that great here, so that's not necessarily the best idea. Your equity will be much more clearly defined on the turn, so I think waiting until the turn is better.
The question is, do you plan on leading out the turn or check-raising the turn. Allowing the turn to get checked through is pretty horrible. Since the pot is pretty small, a single turn bet will be pretty big proportionally (a double bet would be nicer, but I don't think the risk of a check-through is worth it). So I'd simply plan on leading any non-club turn, and check-folding a non-club turn.
If you get raised on the turn, you probably need to let your hand go. UTG+2 can bluff, but a raise against a turn donk-bet on the three-suited board is not all that likely to be a bluff. You have a marginally good hand here with TP3K, but you could well be against a made flush or better J already and drawing extremely thin. The pot is small so getting out earlier is better.
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