Protect...protect...protect your hand

I'm posting the following very simple hand history because I made a crucial mistake that may have cost me a moderate size pot. If I make this mistake again this summer I will cash out my entire bankroll and buy something for my wife (my only poker funds will be when I receive my monthly rakeback payment). She has put up with so much from me. She certainly deserves it more than I do considering I make mistakes like this.

hand #1
9 seated live $6/$12 limit hold'em game.
UTG and UTG+1 play a lot of hands preflop (including any suited cards and any partially connected cards), button and BB are good, solid players.
- preflop: UTG limps, UTG+1 limps, folded to button who raises. I 3 bet in SB. BB folds, UTG and UTG+1 both call 2 more, button caps, everyone calls (4 players, 17 small bets)
- flop: Jc3c4h - I bet, UTG folds, everone else calls (3 players, 20 small bets)
- turn: Jc3c4hAc - I bet, both players call (3 players, 13 big bets)
- river: Jc3c4hAc5c - checked around. I show AsAd, UTG+1 shows Tc9s, button mucks his PP. UTG+1 wins a 13 big bet pot.

My betting the flop here is just plain retarded. Clearly the button will bet if it is checked to him. I estimate a 70% chance that UTG+1 will call 2 cold on the flop, so in fact, it would likely have been best to wait until the turn to check raise. However, my hand was so weak, I probably would have not been able to resist check raising the flop. I think the only high probability situation for me to have won the pot would be if I could have successfully check raised the turn. I'm not sure if the button will bet when the turn comes Ac. (I give him a less than 50% probabilty of betting the turn) So all things considered, I am likely to lose this pot no matter how it was played.
Why am I so unhappy about the hand then? The way I played the hand guaranteed that I would lose the pot.

If I had check called the flop, should I have bet out on the turn? I think that I should for 2 reasons. 1) it is extremely unlikely the button has an A, so he is more likely to take a free card, 2) he has a ~50% chance of having a club (between the 2 opponents, the odds are ~75% that there is a least one club out there) I think in this scenario, it would be best for me to bet the turn.
What about if the flop and turn were played the way it was actually played, is there any value in betting the river? I think I should be scared of the button having either Kc or Qc, but if that is the case, what do I do if I check and the button bets the river? I probably have to call. What should I do if UTG+1 bets the river and button calls? or button folds? I'm not sure if the pot was big enough for me to overcall. It was certainly big enough for me to call.
Probably my only clear fold on the river is if it is bet and raised to me.

Ironically, lately I have always been remembering to protect my much more vulnerable top pair or 2nd pair hands (where my pair is something between 6 and J) on the flop in the SB when expecting the bet from my immediate right.

The button later told me he was drawing dead to me on the turn, and wished he had folded. Ironically, I think his call on the turn saved me from having to make a crying call on the river.

Hmmm, there are certainly a number of different ways this hand could have played out.

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As an aside, what can I assume if the button raises and caps the flop? If he raises, I think the range of hands should be JJ, QQ, KK, AA. There are 3 ways for him to have the nuts, 6 ways for me to have the best hand, and only 1 way for us to be tied.

I am curious about the button's actual hand. Since he capped it preflop, I would have guessed QQ or KK. However, I'm a little surprised that he would not have raised the flop with an overpair. TT or 99 seem way too weak to cap it preflop. If I had to guess, I would go with QQ since that seems strong enough to cap it preflop, but weak enough for him to only call the flop and turn (I guess fearing JJ, KK or AA).