Common spot i suck at

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CC what bet on the flop? 1k? Leaving us 1.2k behind and 3.5k in the pot?

If I check this flop, and I don't fold, then I check shove. Or just shove the turn. I think CC...CF is lunacy.

Edit: I probably wouldn't shove pre here. I think the hand has too much value. So probably 500/call. As played, I'm definitely checking and probably shoving. Worse isn't probably calling UI however we play it but may be dumb enough to bet and then will call. Better probably isn't folding however we play it.