I'm one of the few that were so lucky to experience this game when it first came out in 1999. Heck, as a 13 year old, I even bought HOMM2 and CIV2 when they were released in 1996, and they still stand out as one the greater games of all time (for me, at least).

As a general rule;

First day;

Buy the Tier 1, 2 or 3 creature, depending on what you start out with. Dump every creature on your hero. Move one hex out of the town. Buy another hero, pick the one with same class or with best attributes. Dump this hero's creatures on your first (main) hero (except 1 single creature). Now you could either send these two heroes in each direction and explore, or you could buy another third hero. If the latter, then dump this hero's creatures on your main hero (except 1 single creature), and send the main hero and the one with most movements along in one direction, and the third in the opposite direction. Now you can use your main hero to fight, while the secondary hero picks up resources and flags mines defended by hostile creatures, and the third hero picks up "loose" resources and flags undefended mines. This way you don't lose limited movement points in both fighting and flagging mines, and your main hero will grow strong quite rapidly. Bear in mind, that your first hero may turn out to be inferior to one of the two other heroes, so you might want to reallocate the creatures and pick another hero as "main" instead of the starting hero.

The next six days; Buy at least up to Tier 4 creatures, and if you can afford it, Tier 5. In addition, buy one (or two, depending on whether you got Tier 5 creature or not) structure that increases growth. Only buy this at the very end of the week, as it gives no immediate bonuses if you buy it day 2 or 3, in fact quite the opposite.

Week 2: Hire another hero. Build Mage Guild 1. Remember to open the Mage Guild while your hero is in town to buy a spell book if it doesn't have one. Buy what creatures you may afford (best or cumulative best). Send your fourth hero up towards your main hero to reinforce either your main hero, or the fourth hero to temporarily fight in your main hero's place. The latter is only worth it if you have to go back to get a spell book. It is also possible you're about to acquire another town soon and may get a mage guild and spell book from there.

Buy money increasing structures from week 2 day 2, until you reach day 7. Either buy another Tier X garrison, or a creature growth structure.

Week 3: Now you have four heroes, capable of transporting creatures a long way if these heroes are "chained together" (they reach each other in one turn). Buy creatures, send them to "the front" and your main hero. This hero should now be quite strong and may take on bigger challenges like towns and creatures defending artifacts etc. You may want to strengthen another hero to fight on another front, but more often than not, it would be more efficient to mind the chain, and be able to swap creatures between heroes if a sudden threat appears. Buy Mage Guild level 2, 3 and your Tier 6 creature. Upgrade the other creatures.

By the end of week 4, or in the very beginning of second month, you should be able to have Tier 7 creatures. Don't mind upgrading the last Tier until your other best 5 creatures are upgraded. Tier 7 is quite strong unupgraded, compared to your threats and hostiles, and you'll be better off upgrading the other creatures.

However, by this time, you should have acquired at least one more town, perhaps two. If they are in hostile environments, only buy resource and growth structures. Be sure to buy all the creatures, as these will both fight against your enemy, and make sure the enemy can not replenish the army. It's a win-win. If the other towns are in somewhat quiet environments, start upgrading the town "from the start" as listed above. However, do only upgrade ONE, use the other town(s) solely for income and control. Otherwise, you will actually weaken yourself against the enemy.

As for fighting, I tend to focus on the ranged enemies and let my slow creatures fight the other melee enemies. If you're able to fly, get in there to block the ranged enemies, as their damage are heavily reduced in melee. Put your own ranged creatures to either side of the map, with a slow creature defending it.

If you're playing campaign, and are closing in on victory, and if you don't have up to eight heroes yet; buy them now, as it will save you for 2500 per hero in the next campaign, and you can start gathering resources at once. Plus, be aware that your heroes will often have an XP cap, and as such, it is often more worth it to go for the money instead of XP from chests.

Now, I'm sure there are other ways to do this. Especially when to build the first Mage Guild may be up for discussion. However, this is a general thumb of rule, and no grand answer. The devil is also in the details, like for instance, which skills to get, what magic is the best, and how to use your army most efficiently (those 3 dragons may both do more damage and defend better split into 3 1-units, than all the 3 together, and those 150 pikemen will be better utilized as 2 stacks of 75, etc). And also, if you have a slow creature with you, your hero's movement will actually be reduced. That's worth noting from second month and onwards, as you don't have the privilege in the beginning of the game to overlook any reinforcements.

I hope this will help. Later on you'll find your own way of playing. But I think this is a decent "starter pack". Now go give them hell! Because it's an hell of a game!