Trying to get into this but I am having trouble knowing which battles are winnable before I enter them. It seems like a complete crap shoot whether I will be over- or underpowered for the battle, and I don't see anything in the main map interface that will help me judge. Do I just have to memorize the different enemy types and slowly develop some intuition about this?

In part, yes, you have to get a "feel" for the enemies and how they work. However, if you right-click on the enemy troop, it will give you a rough estimate of how many there are in the bunch:
A Few (up to 5)
Several (5-10)
A Pack (11-20)
Lots (21-50)
A Horde (51-100)
and so on. It gets bigger with a Throng and a Legion (which is 1000+) and there are a couple others in there too. "Lots" is a dangerous number, especially with high-level targets, because the difference between twenty-one and fifty is huge.

The other thing that you can check is the Visions spell. If you cast Visions, it will not only tell you the exact numbers of enemies, but also (in the case of wandering monsters) their probable reaction to you - whether they'll fight (meaning that they think that they can at least hurt you) or run away, talk (if you have diplomacy) or join you.
Beyond that, it's really a bit of knowing the numbers, getting a good feel for the tactics, and save-and-reload. A lot of save-and-reload, until you learn the ropes.

Good advice, thanks.

I'm assuming you know that right-clicking on an enemy and holding down the mouse button will let you see what creatures he has and their rough amounts.

One thing to be wary of is when you see that he has top troops and plenty of them, obviously. The computer doesn't tend to spread the best troops out among different heroes too randomly, but rather will push the best ones onto its most developed heroes. The result is that you need to keep in mind that a good number of top level troops on a hero means he may be the best hero the computer has. And the computer tends to use that hero for fighting as much as possible, developing secondary heroes to explore and grab or retake mines. That's why you will see so many artifacts left alone in enemy territory -- the computer is too busy sending its top guys to fresh fights to pick everything up.

So keep in mind that even if you have a lot of good troops too, you might be coming up against a hero that has a lot of levels and some very good attack and defense stats. If you have used your main hero to do a lot of random exploring instead of fighting as much as possible, you may be more behind than you think.

I tend to play large maps and sometimes don't see the enemy for a while. But when I do see him, I make sure to buckle down and do less traveling for that one extra mine or windmill, and more fighting creature stacks instead of saving them to develop secondaries or to get to later.