I'd start with medium. I always like medium battles in TW because it gives you "fair" historical match-ups on the battlefield - their men will only outfight yours if they are superior etc.

I forget the details in MTW, but "hard" gives a fairly subtle edge to the AI on the battlefield. "Expert" is a bit more blatant, but not as much as RTWs VH battles.

I don't recall the strategic situation varyingly markedly by the difficulty level: you get less cash to start with but from what I remember, it did not feel that the AI treasure chest varied that much (unlike in RTW VH campaigns).

In my opinion, the Risk-type map of MTW (and STW) can make the AI much more competitive than in RTW. So I would try it on medium and bump up the difficulty level on later campaigns depending on how you find it.