$50NL AKs best way to play for stacks w big draw on flop?

Bodog so rough HH:
First or second orbit at the table, neither villian (nor I) have done anything of note.

Me MP AcKc $50
Button $100
BB $50

I open with $2 in MP
Button calls
BB raises to $5
We both call
Pot is $15 going to the flop

At the time I had BB on a narrow range like QQ+ and maybe AK. Never considered Button.

Flop comes JcTc5h.

BB bets pot, so it's $15 to me and I've got $45 behind me.

At the time my thinking was that I have at least 12 outs against AA, 15 against KK and am freerolling against AK.

I min raised to $30 Button thought for a long time before folding, BB pushed and I called.

Thoughts?

At the time I had BB on a narrow range like QQ+ and maybe AK.

So why did you call? If you flop a King you won't be happy because QQ will shutdown all the while taking big fire from hands that beat you. If an Ace flops either you make nothing or get stacked by AA. Will you be happy with a flop of AKx? Probably not because you lose your stack the times he has AA/KK while chopping with AK.

I min raised to $30

Why the hell did you minraise? Push that trash. You want all the money in on the flop. Don't friggin minraise.

Thoughts?

I pokerstoved it and you're a 53/47 favorite against QQ+. You got your money in good job. You played awful.

Yikes, tough crowd

I called figuring that with $3 to win $12 (or $15 if the button calls) and position is good enough for my 41% equity against his range. Plus it's very easy to get away from if I miss. I agree that against an aggressive player I'm going to have a very hard time figuring out if I'm up against AA or QQ on a K high flop.

I also figure that these are the types of hands I need to learn how to play to improve my game.

My intention was to try and come up with strongest way of getting all the $$ in. Your point (which makes sense) is that by pushing he might fold.

I thought I'd play it like I would JJ/TT (which in and of itself may be wrong/transparent).

thanks for the response

I'm sorry if I came off harsh but whatever. This shouldn't be how you play TT/JJ either. If you flop a set here push as fast as you can. You think his range is QQ+/AK so push. Nobody folds an overpair(QQ+) to a push on a draw heavy board like this in a reraised pot.

I called figuring that with $3 to win $12 (or $15 if the button calls) and position is good enough for my 41% equity against his range....Plus it's very easy to get away from if I miss

This has reverse implied odds written all over it.