Catching a piece of the flop from the blinds

[SoCalPat]

It's one of my favorite plays, but I'm wondering if I'm approaching it right.

For example, let's say I'm holding T6o in the BB. I check the option behind 6 players, including the SB.

The flop comes KT7 rainbow.

UTG bets out and gets 3 callers. I can close the betting and I'm getting 10-1. Easy call? What if there's a two-flush on board, or if the board comes JT5 rainbow? If I improve, go for the check-raise on the turn? I've been calling and going for a turn C/R most of the time here, presuming I improve. What if I don't improve? What odds do I need to see the river?

What if a MP player bets out, I'm getting only 9-1 and there are two players left to act? Still call? If I improve, bet out on the turn? Or go for the C/R if it can reduce the field?