Battle for Wesnoth

It's a cool game, especially great considering that it's free. Keep in mind the terrain and time of day and you'll do fine, most of the time. RNG will really fuck you at times, so be ready for that.

Please continue.

Expect certain cool campaigns to be unfinished (like the becoming a necromancer one)

Getting flashbacks here

If you liked Heroes 3, make sure you check out Disciples 2 Gold and the Age of Wonders series.

It's fun and there's plenty of custom campaigns to play, also a skirmish mode and MP if that's your thing. The RNG can be a little annoying but it honestly isn't as bad as many anons would have you believe and it doesn't matter in MP since both sides are equally prone to it (in SP it hurts the player a bit more than the AI for various reasons).

If you get the chance always level up a caster up the healer patch first (you can make the second one a damage-focussed caster).

And Mage Knight. I'm becoming tempted to start offering to teach the damn game in these threads just because of how worthy of a successor it is. There's also a Star Trek version now if that's your thing. Either of which are practically a direct sequel to HoMM in terms of gameplay.

path* not patch

Have you played Master of Magic, Eador: Genesis, or the Age of Wonders series already?

-Typical level cycle is you capturing a bunch of villages at the start, recruit or recall as many units as you can, and carefully march towards the goal. Don't expect to be able to get reinforcements, as almost every level has a time limit against you. Your enemies won't send reinforcements either until you start killing off his units, and even then usually only one at a time.
-There's a button somewhere in the options that lets you see how much gold your enemy has. This can give you an idea of how many units you can expect to face.
-Try to stick on good terrain and force your enemy on bad terrain. The AI tends to be more suicidal than you (by the way they also like to pick on low HP units so keep those away from the AI).
-Try to keep your loyal and free units alive, as they don't cost upkeep.
-Put your level 1 units in front of your higher level units so your higher level units don't die. Protect your units that are about to level up. Try to feed kills to your lower level units.
-Try to stick your units on good terrain.
-Try to hit melee units with ranged attacks, and ranged units with melee attacks.
-Abuse leadership to get as much damage out of your units as you can. Your hero unit usually gets leadership when he levels.
-If possible, avoid going full-out attack during the cycle of the day that's disadvantageous for you or advantageous for the enemy. In general, you should attack at dawn (your enemies are usually chaotic).
-Orc assassins are a fucking shit to deal with.
-If you can, try to get a white mage so you can hold the line better.
-When upgrading horseman, always go knight.
-When upgrading elf archers, always go marksman.
-Archers and spearmen and horsemen suck against skellies.
-Don't bother using too many scouts except for taking villages.
-Don't play on hard mode unless you like being forced to save scum a lot.
-You get a full heal when you level up. I forget whether or not you still get a full heal when you reach max level (I don't think you should but they might have changed that).
-Try not to drag out levels too long. I think the gold bonus is calculated depending on the total number of villages and number of turns you have left, so it's always more optimal to end the level earlier. If you fuck up and don't have enough gold for the next level be prepared to rely on a really small army.