The rule I use in mixing troop types is: how many of each type am I facing. It's 1, 2, or 3.
If it's one type, that's easy. You have something that is strong against that. Use it.
If there are two types of troops in the enemy armies you can generally stick to one type of troop. Even if the type of troop you pick is only even with some of the enemy troops. For instance, when facing 4 mages and 2 light melee I would pick 5 cerberus (dogs) because they are great against mages and even with light melee (which is what they are). 4 light melee and 2 mages would probably get 5 heavy melee because they are good against the light melee and can take a licking from the mages even if the mages are supposedly strong against them. I've always found the light melee/mage combination in enemies difficult, btw.
In any case, if there are three types things get trickier. Of the three types I find that if there is only "one odd" I can pretty much ignore it and stick to the thing as if there were two types alone. If there are three types and they are split pretty evenly, like 2,2,2 I, again, ignore the weakest type (usually mages) and go with 5 of whatever is good against the other two.
The most difficult combination is when you have 3-3-2 and the "2" is really strong against whatever you are throwing at the 3-3 types. In that case I might go 3 (against the 3-3) and 2 (against the 2). However, I find the order you put them in seems to make a difference and, unfortunately, it gets quite complicated. Usually the difference isn't enough that you lose, but it does, sometimes mean you lose more troops then you would have done had you ordered your troops the other way. Instead of putting the 3 light ranged first, then adding the 2 blossom mages, you could have put the 2 blossom mages first, then the three light ranged. It all depends on the order of their troops AND the terrain. The order of their troops you know, but the terrain you don't and won't if you auto-fight. Since I usually auto-fight it's a bit of a crap shoot when it agains 3-3-2 and the two is strong.
In the end there is no formula that makes it easy, but experience does eventually hone your instincts and instincts, properly honed, do improve the odds. So just keep fighting and you'll get there.
AJ