Your betting here baffles me. Bet and get called, check and call a bet, bet and get raised... how do you have any idea where you stand? Also - how many people were at this table? I typically raise with tens. With a min-raise and a bunch of folds, I might even re-raise. I'm more inclined to re-raise with fewer players though. Was this a full ring or what?

Better lines than yours:
1. call the pre-flop; bet the flop and turn; check/call any reasonable bet on the river.
2. re-raise pre-flop; bet the flop and turn; check/call any reasonable bet on the river.
3. call the pre-flop; check-raise the flop; bet the turn; check/call any reasonable bet on the river.

All three of these assume the same board as you actually got in this hand. If the turn and river cards are king, ace, it's probably safe to let it go.