What's an idiom for the action of going for the most likely / most appropriate option? I had been saying "placing my bets with _" but it turns out that doesn't exist :D Must have got it from "hedge your bets" which I don't think means the same thing - also, what does this mean?
As John Lawler points out, "betting on" is the correct phrasing to communicate which outcome you are supporting or predicting. If I understand your question correctly, it is only missing the element which identifies your choice as having been chosen for being the likely winner.
A likely outcome, in betting terms, is a safe bet. It is difficult to suggest a construction without any context, but you might say "I consider X a safe bet," or "I'm going with the safe bet."
"Hedge your bets" means to position yourself to benefit regardless of the outcome by betting on both sides of an issue in an effort to play it safe.
OP could say he's betting on the favourite, I feel that often emphasises the speaker's lack of courage (cf nothing ventured, nothing gained - i.e. If one takes no risks, one will not gain any benefits.)
I'd suggest playing it safe, which to my mind emphasises avoidance of a downside if you're wrong.
If the intention is to denigrate an "unadventurous" choice, there's always going with the herd.