If you are chasing high multipliers just for the sake of winning the high multiplier contest, then the best strategy is to make small bets. Just bet with the smallest amount allowed (make sure to read the contest rules, some of them may require a relatively high min bet amount). This way, you will be able to make more bets which means more chances to hit a high multiplier.
For leaderboard contests, which are harder to win, the best strategy is to play games which have the highest RTP or the lowest house edge.
Yeah, you're right. And about the betting limit, I think contests wouldn't have a high limit for what your bets should look like; however, if they specify that you have to play certain games, then the lowest betting amount of those games might create problems for you if they don't allow betting with smaller amounts. Most slots would allow you to bet $0.1, or maybe $0.2, which isn't that high.
About your second point, I think you are still going to lose a good amount of money even if you are playing games with a higher RTP because slots are unpredictable, and sometimes you might hit a good multiplier very early, maybe within 20 spins, and sometimes you don't hit anything even with 100 spins or more. The RTP in most games usually hit you up with a win in another session, so if you gamble $20 in one sitting, you might get some wins in the next session if you play the same game.