For MM:
I skipped 1-2 as I didn't want to play stickman graphics. They are of one style.
I played 3-5 and loved the art style. IIRC 4 is the first game I ever played where we got a base. 3-5 were an upgrade from 1-2.
I played 6-8, which were the next upgrade. IMO 6 is the best, and 7 is good. 8 suffered budget cuts and isn't completely finished. 8 also forced you to have a monster party instead of standard peeps, so you may love or hate that.
9 is an abomination. It's its own style as this was the end of 3do and new world computing. The world is empty, the setting bland... the only thing I liked was the class promotion system. Otherwise, gamers pretend MM9 doesn't exist like people pretend Ultima 9 doesn't exist.
For HoMM:
1 is crude, 2 is fun but a bit unbalanced. Art style is the same as MM3, which I loved. 3 adds more to the towns and balances and fleshes things out more. H3 also has the largest modder attention I believe, with first WOG and now Era. There are tons of maps for H3 and that's what I would suggest. You could always try the H2 demo if you wanted, which is what sucked me in to the HoMM games in the first place.
I've never played 4+
Dark Messiah was a HUGE disappointment for me. When the companies went under, Ubisoft paid millions for the MM brand. They slapped it on Dark Messiah when it really has NOTHING to do with the MM games, not in style, setting, tone, or anything. The MMs are rpgs, the HoMMs are strategy. DM is an action adventure. I bought DM based on it being "of might and magic", and felt betrayed to learn it was just a marketing trick. I've been pissed at Ubi ever since.
So for MMs I suggest MM6, and for HoMMs I suggest H3. As always, I suggest watching lets plays to get a feel for gameplay.