1. Raise 3x with the intention of folding to a push, and playing cautiously on the turn after a call.

Hero has a very strong, but vulnerable hand here. Basically we're only worried about AA-QQ and a rogue 8. This is where reads come into play, but you said "random player" so I will interpret that for these purposes ot be "average player." Average player reraises preflop with AA-KK. QQ is unlikely for obvious reasons, so we are really only worried about a hand like 89s or A8. Whenever someone bets into me after I raised preflop on a flop like this, I generally get a little suspicious. Usually they bet like that because its unlikely I hit this board. But they could be trapping me with an 8. They could also be doing this with JT or QJ. Since its hard to know where you are at in this situation, I like to raise and find out while the pot is small.

2. Raise 3x with the intention of folding to a push, and continuing to value bet on the turn if checked to, or call another bet on the turn if bet into. The draw increases villains range to more hand that I beat.

Same as above, except you get more value because a FD will typically call you down at least to the turn.

3. I fold here. I don't care for messing with second pair on a K high flop OOP too much.

4. 80% fold, 20% call depending on read.

5. 80% fold, 20% call depending on read.