I'm quite flattered. Especially given that I rely on screenshots much more than actual writing in those AARs
Now, you have basically two choices for determining what constitutes "good" gameplay. The reported scores and whether you achieve the goals you set for yourself. I will focus on the "formal" scoring.
For the scores, two things matter. First of all, you should do all the usual things to maximize your score - that means winning battles and annexing territory. If you're playing a religion (such as Sunni Islam), spreading Islam (and making your secular nations help) will do the same. There are other ways to earn points, but these are very reliably. Of course, if you care about the point totals, note that beating up one of your own nations won't contribute much to your total score, because you will be winning points for one nation at the expense of another.
Secondly, you get points for controlling regions that were historically conquered by a particular nation. For example, you get extra points for controlling Italy as the Ostrogoths. The information on the historical regions of any of your nations is in the ledger.
Apart from this "formal" score, how well you play would be measured by how prosperous/powerful you are (just like in any Paradox game). Clearly, for barbarians "becoming powerful/prosperous" is synonymous with migrating to the Mediterranean and taking the richest land you can find. The Western and Eastern Roman Empires are already prosperous and powerful, so your job is to keep out the barbarians. That's really all there is to the game.
Of course, there's about a million other factors to consider. But these are all subordinated to the task of keeping your nations powerful and prosperous. If your kingdom suddenly finds itself with a Muslim majority, converting to Islam makes strategic sense - it cuts down on your admin. points expenditure and prevents revolts. Protecting caravan routes from bandits and raiders helps your treasury (which in turn helps you raise more armies). There are many things of this sort, but the way to think about any decision is - "does this make my nation more powerful?" If you become richer/more stable/strong because of it, it's "good gameplay."
To really get into the game, I would suggest concentrating on a single nation in some scenario (by turning on the AI for everything else). Try the Huns and see how well your armies knock out everyone they come across. I've noticed that stratagems and leader abilities are often more important than anything else - which may explain why you have such trouble with WRE.
Strictly for the WRE, although I've never played them, I think there are some natural suggestions -
1) You have a navy, so use it. You can shuffle armies around from Africa to Britain, while the barbarians can't. You can also use the Eastern Roman Empire's forces to help you out (since they're one the same team).
2) You can simply avoid fighting altogether (aka, the historical Roman way of dealing with barbarians). I can't think of any place that the WRE should conquer, because everything outside of the Roman Empire and Mesopotamia/Persia is basically uncivilized wasteland devoid of infrastructure and full of angry natives. Just keep using bribes, tributes and stratagems to prevent the barbarians from ever invading and deal with the numerous event-driven revolts in the meantime.
3) Use space. You have a lot of land in Rhaetia, Illyria and Gaul to trade for time, without significantly damaging your income base.
4) Expect defeats. Sometimes very dramatic ones. But don't push it - there is a retreat button for a reason, you don't have to fight every battle to complete and utter annihilation. Over time I learned to like the randomness and harshness of the battle engine.
5) Offer barbarians border province to make peace, then retake them when they lose control 10 years later.
Non-specific advice (not just for WRE)
6) Use the ledger to find out the best general your have and appoint them to lead your most important armies. This is crucial, because barbarians often have leaders with very high skills.
7) Use in-battle stratagems to gain the upper hand. For example, some barbarians (like the Huns) have cavalry far superior to whatever Romans can field at the beginning. But you can use a stratagem to double your cavalry's shock attack (if successful) and thus counter their cavalry with your own.
8) In connection with the above, mixed armies have an advantage, because having more heavies/cavalry/archers than the other side gives you a bonus.
Usually I can figure out just about any game before reading the manual, but I have never really grasped Great Invasions. I never know why my victory points are so low, or what I'm supposed to do with the Jutes/Goths/etc etc.
