Tough poker hand

Game: $1-$2 $100 buy-in: 9 players
3rd hand –new table

The 1st player under the gun made a raise to $8. Everyone folded to me. I was in middle position with the JJ and raised to $24. The button called the raise. The initial raiser under the gun folded. There were only 2 players going onto the Flop

The flop was rainbow K rag rag: I checked, the button went all in (he had $96) and the action was on me.
Since there was a K on the flop I was hesitant to call: but since he called my raise from the button I could not put him on anything. We only played 3 hands there was no way for me to determine his style of play.
I asked for time then called. Fortunately, the button was trying to steal the hand. He sensed weakness in my check. Also his all-in bet here was a good sized bet. The K on the flop was a good opportunity for a good sized bet to make a steal. My JJ held up.

How would you have played this hand? Please give me your suggestions.