Hey,
You should check out Battle for Wesnoth (www.wesnoth.org). It's a free, very polished turn-based fantasy game and has all the qualities you listed. I've enjoyed it a lot. Very active community too.

I'm really loving it so far. It brings back some of the HOMM2 fun I remember from years back, but with a darker feel and interesting leveling choices.
It's definitely tough though. If I remember HOMM2 correctly, you could have difficulties, but if you were able to squeak a little ahead and get a superstack going, your chances improved a lot. In Disciples 2, you can take a very strong hero for granted after less than a handful of levels, but still might be faced with what feel like overwhelming odds anyway. I've had to do a fair amount of loading up old save games from well back of my present turn in order to figure out alternate ways of doing things. And the introductory/instruction materials on how to play aren't all that good, even out on the net.
Fortunately, the game is good enough that taking the wrong turn and having to replay isn't aggravating. Some games have missions you grow to hate and just want to finish. I'm not too far in, but so far even when I'm bumping into a brick wall, I'm still having plenty of fun trying to figure out a way around it. I like that so far the missions don't seem excessively puzzle-like, where you have to guess what the designers wanted you to do and then jump through that hoop. You're free to largely play as you like instead of marching like a robot down a straight line.