I try to get 2-3 of the resource cards out in the first round. They become less common/impactful if you get them later. I feel like getting more than four gives you a pretty bad chance of having a terrible/vulnerable setup for round 2. Particularly to a card I think is called Catapults. Regardless it has some sort of siege weaponry on it. It does 3 damage to the first position item. This is devastating if you get it off on someone's resource in round 1 or 2.
Ranged weapons are really good at denial, and I find Ongers to be an insanely good card. So it might behoove you to grab a stronghold type card if you see one, since it completely negates it. I find cards that combo like Trade Outpost (I think, I'm terrible with names) which gives 2 culture to every resource type card, or going military heavy with cards like Shield Wall or the ones that get buffs in the presence of a small number of infantry are really good. I try to avoid things that require the presence of three or more of a single type of card though.
It's interesting that you said the AI hasn't had much military. I have found the opposite to be true. They're really fond of knocking my guys out. I
If you want to try out cards with skulls, try playing with a different rival. A couple of them have guaranteed skull cards. The pirate guy is pretty cool.
Also, make sure you're assigning damage well, and don't be afraid to take some knockouts. You can get rid of 9 damage with a 1 and 2 armor card! (Block 9 with 1 -> halves and rounds down to 4 and block with 2 -> 0) If you have a high armor stronghold, use it and knock it out with another card or two. That way, it has a chance of reviving back up to its normal armor minus 1. If you don't knock it out, it can't heal, and you're stuck with some low armor crap. Destroyed cards can make good shields in the 4th round since they can halve the damage of anything with only 1 armor point. If you only have one knocked out card, it has a 100% chance of getting destroyed. If you purposefully knock out something else, then it jumps down to just 50%. I know that's obvious, but it took me so long to make that connection in my play.
I'd say learning how to assign damage and not being afraid to knock stuff out was the biggest increase in results that I got.