Part: Part Two - Playing Styles & Starting Requirements

Kicker trouble

Pre-flop
Blinds 100 / 200Pot 500 (2.5 BB)BTNKJ 25,000 (125 BB)YOUto actMP 25,000 (125 BB)LimperlimpsSB 25,000 (125 BB)posts 100 (0.5 BB)BB 25,000 (125 BB)posts 200 (1 BB)D

One player limps and it folds to you on the button with K♥J♣. King-jack offsuit is a decent but easily-dominated holding - a textbook 'trouble hand'.

A limper; you're on the button with K♥J♣. Best play?

WhyK-J offsuit wants to be heads-up and in position, not sharing a limped pot with three others where every better king dominates it. Raising over the limper thins the field and seizes the lead - but carry a note into the next streets, because that jack kicker is exactly what lands this hand in trouble.
What happensYou raise to 700 (3.5 BB). Only the big blind calls. Pot: 1,600 (8 BB).
Flop
Heads-upPot 1,600 (8 BB)K73BTNKJ 25,000 (125 BB)YOUtop pair, jack kickerBB 25,000 (125 BB)Big blindchecksD

Flop: K♣ 7♦ 3♠ - top pair, but only a jack kicker. The big blind checks.

Top pair, jack kicker, on a dry board. Best?

WhyTop pair on a dry K-7-3 is worth betting - for value from worse kings and pairs, and to charge the odd draw - but the jack kicker is the reason to keep it medium rather than big. You want calls from the hands you beat without swelling a pot you'd hate to play for stacks against a better king.
What happensYou bet 900 (4.5 BB); the big blind calls. Pot: 3,400 (17 BB).
Turn
Heads-upPot 3,400 (17 BB)K739BTNKJ 25,000 (125 BB)YOUtop pair, weak kickerBB 25,000 (125 BB)Big blindcheck-raises to 6,800 (34 BB)D

Turn: 9♥. You bet again and the big blind check-raises - a big move on a board with no obvious draw completing.

Facing a check-raise to 6,800 (34 BB) with top pair, weak kicker. Best?

WhyA check-raise on a nine that completes no obvious draw is a big, honest move - it's a better king like K-Q or A-K, two pair, or a set, and every one of them has your kicker crushed. K-J flopped well, but 'flopped well' and 'good enough to stack off' are different things. Folding here is the whole point of a trouble hand.
What happensYou fold and he turns over K-Q - the better kicker you feared. Nothing won, but the stack a call would have shipped him stays in front of you. That's a trouble hand played right.
You played the trouble hand by the book: isolate in position, size your value bets to keep the pot manageable, and lay it down when a turn check-raise put your jack kicker on trial. The trouble with a trouble hand is that its top pair is hard to fold - the skill is folding it anyway.

Trouble hands like K-J flop the kind of top pair that's easy to fall in love with and easy to be outkicked. Keep the pot small when you're good, and fold when real pressure says a better kicker is staring back.