On random maps playing as Barbarians, I play roughly like this (at 160%)

Starting hero is either Craig or Gurnisson.
On day 1, build hippogriffs in the castle.

On 1-2-1, take 3 bears and go collect everything available. The goal is to upgrade them and obtain mass haste. Upon meeting the opponent on day 3, 5 grey bears and mass haste should bring victory.
Regarding units:
Gobs — hardly count
Wolves — super unit
Orcs — weak
Ogres — the tankiest 4th tier (attack and damage are just super!)
Birds — cool unit (speed and ability are super)
Cyclopes — almost none (usually not built)
Bears — the strongest 7th tier.

Greetings to Guru Forrest. Guys, listen to what he says, because he plays Heroes like a pro and knows what he's talking about (actually, he doesn't play here, but on Heroes.by; it's very useful to read the game reports of players there, you can learn a lot of new things).

I'll clarify a few things, as I don't entirely agree here...

Firstly, it's not mandatory to build hippogriffs with a castle on day one no matter what. If you see that you have very little money and have the option to either build something else or buy additional heroes for scouting and chains (and properly constructed chains are the key to a very strong game), then always choose the heroes. Furthermore, there is no point in building hippogriffs if, after building them, you will have absolutely no money for several days, while you have already scouted cans, hives, or treasuries; in this case, you will lose a day or two of game tempo because of the bears, and when playing against a strong opponent, this is like death!!!!! Therefore, it is quite enough to stop at building birds, orcs, and ogres—not necessarily with a castle—but instead, by upgrading birds and ogres on day 7 of the first week and day 1 of the second week, and immediately buying up the entire spawned army with the money saved from building hippogriffs and the castle, you will immediately rush to level up on the first day of the second week, break cans, hives, and use the meat obtained there to take everything else (up to the depths). By the end of the week, with a huge army and stats, you will arrive to kill the opponent, who by this time has nothing, since they spent the entire second week continuing to collect freebies from the respawn and nearby and fighting small battles, as they had no money to buy an army because they spent it all on the first week building level 6 or 7 units with a castle (if it's an average player), or because they have no army at all and only just started building it since they went into economics on the first week (Town Hall, Municipality, Capitol) (if it's a weak player).
But... If on the first week you managed to collect/loot enough money so that the leveling tempo of the main hero and the exploration of the territory on the first week doesn't drop, and you have enough money after building hippogriffs with a castle to fully buy them out by the first day—then you must build them without question (and also, of course, in the case where you didn't find anything interesting on the first week that can be broken on the second week except for weak monsters guarding passages and money, and you simply don't need the full army buyout in the first days of the second week—then you can boldly spend all the cash and resources on the first week's construction and put in the bears with the castle with your last coins).

Next, other good heroes are Gundula, Dessa, and Terraxor.
The first hero is good because her specialty is Attack, and at a high level, she becomes a total cyber-killer (like CraigHack), but the advantage over the latter is that Gundula already has slow in her book, and very often Earth is given at early levels. I think no one needs an explanation of what mass slow does in the early stages of the game (especially in the first week). And just slow often helps a lot on the first week or the beginning of the second.
Dessa is a hero specialized in Logistics. It is recommended to take him if the map or template is played where opponents won't meet soon, which gives a colossal advantage to a logistics hero in such layouts; at high levels, he runs twice as fast as a normal hero, and accordingly, he manages to eat twice as many goodies and level up twice as much, which will eventually lead to victory over a hero who might be more powerful in specialty but is slower.
Terraxor is a hero whose specialty is wolves. Forrest wrote that wolves are a super unit, but didn't explain why. Wolves become a super unit when they are upgraded, and if the starting hero is Terraxor, he comes with three stacks of wolves + they get +1 speed. As a result, at the start of the first week, you get 30-50 crazed wolves, with which he can take level 1 cans in the first days of the game with minor losses, break through hordes of archers and level 5-6 caches almost without losses (because Terraxor's starting skills are Attack and Tactics), and break any dwarf settlements (takes even the maximum ones without problems or significant losses). Many strong pro players choose him right from the start for this breakthrough power, preferring him over other heroes. If you play as this hero, for the first two days of the game, you will need to upgrade goblins and wolves (if they are available); if not, then on the third day, fighting initially only with goblins and orcs from the second hero and the left army from the third, but once you finally get the wolves, you will sweep everything in your path.