The chart provided is a good step, and useful for preparation. In autofighting I survey the types of troops and fill my slots with the best troop for the enemy in front of them. Which means, I aim at their center, left of center, right of center, far left, then far right. I'm not sure it's the best pattern but it does seem to have improved my troop victories.
The method I use has some caveats, but in general I work from the highest province I've done to the lowest. I do this because I usually pick a mercenary camp or training camp 5 star against it's opposite troop. Since that means I usually have two choices, I then look at the secondary enemies against my troops. So if in the center slot there is a heavy melee I have two choices, Blossom Mage or Poison Dryad. If, in another slot I see another heavy melee or heavy ranged, I pick the Blossom mage as it's secondary target is Heavy Melee. If I see mages I pick the Poison Dryad because it's secondary strength is mages. I then continue through the five enemies. As I said, though, there are some caveats.
First, about province 20, as I move down, I switch to Barrack troops as much as possible. This helps me maintain enough of the other troops for the next rounds.
Second, if I'm facing either dogs or the mist walker. If even one of those is present I choose with a little more care. In those cases I look for whatever is the "single" type (meaning the type that has only one) and ignore it, unless it is one of those, and shift to a more defensive posture. This means I may choose to use my Poison Dyads against heavy melee because they are at least even with mist walkers and that means I can survive better and use them against mist walker as well. For the dogs I generally don't use frogs but, instead, switch to my Gruff Orc Warriors. In other words, I adjust to handle what I've found are the most difficult for me.
Third, along the same lines I look at the heavy ranged. My Ghastly Banshees are supposed to be good against them, and are, but they also seem to be pretty weak. So I watch for things that can hurt them easily, especially dogs, and if the dogs are present I use Vallorians. Again, the point is, you have to adjust a bit in some circumstances.
Finally, if I'm running short on some needed troops, I find that by starting at the highest province (after the first round, of course) gives me a psychological advantage of feeling like things are getting easier (I know my troops don't have feelings, but I do and it encourages me to think I'm doing okay.) and since the provinces I've done the hardest and can afford to use troops that would get destroyed at the higher levels in place of the ones of which I am running short.
Fourth, if the number of troop types is low, (1 or 2) I consider using only one type against them as the AI seems to do better with fewer types.
So, for me, in the end, it's about making the best match you can and watching troop balances so that you have the troops for next week you need.
AJ