Although it lacks a progressive jackpot, as does Caribbean Stud, or decent sized payoff for a royal as in Let It Ride in a casino environment, I would recommend of the three, Three Card Poker, simply because the casino advantage is lower on select bets among the three games you mentioned.

With Caribbean Stud, the best you can hope for is a casino edge of about 5.2% based on the player's ante wager, or 2.6% based on the ante and call bet. As for the progressive wager, the average house edge is over 26%, depending, of course, on the size of the jackpot.

As for Let it Ride, even if you played the game flawlessly, the casino's edge on Let-It-Ride is 3.51%. And, oh! let’s keep track of those Let-It-Ride side bets where for $1 you are offered an additional payoff with certain paying hands; those bets carry a double-digit casino advantage.

As regards Three Card poker, it depends on whether you like your cards or not; I’ll rephrase that—on whether youshouldlike your cards. The house edge is 3.37% against the Ante alone, but only 2.01% against your Queen-6-4, if you decide to make the Play bet. With a Pair Plus wager, the casino advantage is slightly higher at 2.32%.

As you can see Three Card Poker offers better wagers for the player, and although the casino advantage is above my suggested “never make a wager that has higher than a 2% house edge,” it is tolerable, easy to learn, and plenty of players find it fun to play. 

However, you knew this was coming, didn’t you? ….You might want to think about giving Mini-Baccarat a try, or even blackjack, using perfect basic strategy. Each has a house edge well under two percent, beating the bejeebers out of all the table games mentioned above.