I know only HoMM2's original campaigns (Archibald and Roland), which I very much enjoyed playing years ago. (I've just bought the game from GoG so as to replay these campaigns on my modern system, and as a bonus can now follow them with the expansion campaigns.)
In those campaigns your choices serve as difficulty settings. My opinion: for the easiest run through Archibald's campaign, for example, choose #4 (alternative to #3), #7 (optional) and #10 (alternative to #9). #7 is a walk in the park with an award carrying over from #4, but practically impossible without (i.e. after #3). Then each scenario has its own three options, maybe sometimes there's not much to choose between them but sometimes there is, e.g. Archibald #2 is easiest with barbarian.
The beauty of those campaigns is that different plans work better for different scenarios, but in general, don't just explore and exploit your starting area, but remember you are in a race against the computer to get what's in the middle, not to mention beating it before it beats you.
If you get stuck, YouTube has plenty of "Lets Play" recordings by people showing how it can be done.
My own tip (in HoMM2, but maybe it will apply throughout the series), is when attacking the mobs of creatures littering the map and getting in your way, knowing which to attack with what you now have and which are dangerous is key, but do leave room in your army for them to enlist with you if they want to. You can always reject them if you want a fight or think that particular lot will be a liability.
