As far as I know the AI in AOW 1only "cheats" when you play on the higher difficulties or when playing a scenario where the AI is given an advantage from the beginning or later in the game. Most of the scenarios in the campaign probably works that way. Story driven scenarios that you can download from Heaven Games often also employ this to give experienced players more challenge as well as surprises.

What I would recommend for you is to download some multi-player AoW 1 maps from Heaven Games and play them as single player. That's the way I play Age of Wonders the most. The campaign has a great story but there's just something about several empires starting out small, building themselves up and clashing in a great war.
You can make up your own story as you go along or just play it purely as a strategy game without any user created story and events getting in the way. Some of the map-makers are brilliant at making maps with beautiful terrain. I could recommend you some maps, but since I mostly play XL maps it would be more useful for you to browse the large and medium maps at:
http://aow.heavengames.com/downloads/lister.php?category=multi

I just play by the vanilla rules myself. Most AoW 1 maps are made for the vanilla rules the map scene is quite different from that in AoW: SM with all it's mods. The AoW 1 map scene should be less intimidating for a new player.
In additions to the vanilla rules (AoW 1) there is mostly just Warlock's rules and Lighthawk's rules, which is an expanded version of Warlock's. I haven't used those myself yet, but as far as I remember they are not radical changes, just some new units, some re-balancing and some changes to make the heroes a wee bit less overpowered.

As far as AI, "cheating" and difficulty goes it is supposed to be like this:

Human Player +0% gold/mana +1 XP per turn
Squire +0% gold/mana +1 XP per turn
Knight +50% gold/mana +2 XP per turn
Lord +100% gold/mana +3 XP per turn
King +150% gold/mana +4 XP per turn
Emperor +200% gold/mana +5 XP per turn

(+ XP per turn is the XP bonuses all heroes get each day whether they are fighting dragons or sitting on their asses)

So unfortunately the most fair game against an AI economically would be on the lowest difficulty. But since the Squire AI is so timid, I would not recommend to go below difficulty Lord at least. Try with that and if it becomes too easy just raise the difficulty. At least in this way you know from the start what bonuses the AI has, unlike many story based scenarios where the AI may get some unexpected help from the designer later in the game. I don't think giving the AI bonuses should be considered "cheating" since the rules are predictable. The player can learn to manage his empire, hero development and tactical battles so much better so it is only "fair" that the AI gets some bonuses to help it. With the exception of these bonuses (and that it probably can see the whole map) I think the AI plays by the same rules as the player. The difficulty level may also influence the aggressiveness of the AI or it may just be that it gets bolder when it has a better economy.

It would be nice if they spent a lot of time and resources into creating a good AI in AoW 3 (but still kept the higher difficulties with AI bonuses). I think it actually is possible even though almost no (turn-based) strategy game have it. It seems like it is too difficult for most the designers to implement and besides, AI is almost never a huge priority anyway.