I'd like a line check/thoughts on this hand. I'm happy with how I played it, but am curious how others would play it, or if I should be playing it differently.

Blinds are 100/200/25

Hero - Hasn't played many hands, so not much will be known about me other than I'm from Canada and was wearing a REGCharity patch, which I think effected how people played vs me
V1 - First hand at the table. Know absolutely nothing about him.
V2 - Middle aged european guy. Does not like to fold. Definitely the fishiest/weakest player at the table.

Hero - BB
V1 - UTG+1
B2 - BTN

(2850)
V1 opens to 500, 3 callers and I defend Kh9h from BB. Flop is Th8h5c. Hero checks, V1 bets 1200, folds to BTN who calls and Hero calls.

(6450)
Turn is 7s, Hero checks. V1 bets 3700, BTN tanks for nearly a minute before calling, Hero calls.

(17,550)
River is Js, Hero shoves 15k. V1 mucks very angrily, V2 tanks for 2 or 3 minutes before folding.

V2 claims to have had a set. So, as mentioned, I'm happy with how I played this hand, and am mostly curious about others thoughts.

Should we be check/raising on flop or turn?

How about the river, should we just check and let one of these two bet? I'm not sure what V1 has that he's going to barrel again, but if V2 had the set, then it's plausible he shoves.