For each race, you need to use a different approach, although in most cases, one method works. For dealing with melee units, it's quite simple – if you have fairies/furies, you shouldn't have any major problems, except perhaps with melee units with high initiative. But there aren't many of those at the early levels. If you don't have either of those, then you have a hero who shoots magic, or decent ranged units :) or you're a Gnome (Necromancer) – thick and numerous :)
You can take a hero with a ballista at the beginning. Heroes with ballistas, as you know, deal with neutral creatures more easily.
In battles with enemy ranged units, the Dungeon is the easiest.
Use invisible stalkers and shoot them down with заклы (zakly), followed by finishing them off with your first units.
When playing as Inferno or Academy, etc., you deploy thick troops, such as demons, gargoyles, zombies, armored units, etc., and then shoot with a ballista/заклы (zakly)/or engage your troops in melee combat. Therefore, at the early stages of the game, these seemingly less useful troops play a crucial role and die in huge numbers. Although it's not a pity to lose them.
The Necromancers are very lucky here; the new skeletons are great for dealing with ranged units.
To deal with mages, again, you need to deploy thick troops, preferably with magic resistance. Although this is more difficult.