Research

Primary research gain is from number of cities and level of cities. If you are not expanding enough you will fall behind. If you are not leveling your cities fast enough, you will fall behind.

Infrastructure comes next. Building Unrest reduction reducing buildings will give you the full research gain from your cities. Building +research buildings in conclaves will give a massive boost.

Followed by Inspiration Enchantment if you have access to it. Exploring fast and aiming for lost libraries if available.

You need to remember trading for research usually comes with losses. If you trade enough with everyone you SHOULD come out on top. but I think all you'll end up doing is being tied for equal top with each player that has the highest research. While making them catch up with research that is lacking.

For research goals try not to waste time on things that take too long, so if you are yet to expand, aim for all the easier researches, that way you can benefit from them ASAP, then go for the better ones once their research time is more manageable. Build Conclaves even if there is no/low essences bonus instead of a town, since you can throw libraries and other research buildings into it.

I hope that helped or helped you narrow down what it is you need help with. More information would be useful.

Thanks for the comments. I pretty much do those things, except expand fast enough, but that presents me with a problem. Whenever I expand as quickly as possible, I invariably lose cities to wandering monsters. That has led me to follow this strategy, I settle two cities at the beginning. I then clean out the monsters, etc., in the area. I then settle a third city, and do the same thing, etc., etc. However, though that leaves me with cities that are safe from monster attacks, I find myself falling behind. It appears to me that AI civilizations expand as fast as possible and establish as many cities and outposts as they can without worrying about losing them to roving monsters.

I have been playing on hard and the AI crush me in research.  I feel I expanded really fast in my current game and am doing really well all in all, but half the AI is twice my points in the faction power rating and their research is well past mine.

What do people use as a rule of thumb ratio for towns to fortress to conclaves?  I normally go something like 6 towns for 1 fortress and 1 conclave.

Also, what type of tile is best for a conclave?  Let's assume all available choice tiles have 2 essence on them.  Would you pick a 3 food/4 material/2 ess or a 4 food/3 material/2 ess or a 5/2/2 or a 2/5/2, etc? I am just trying to get a feel for the best tiles for conclaves.

I'm relatively new to FE though my current game is on hard and essentially won but I'm planning on coasting to the turn limit for the achievement, hehe. I never lost the faction power lead and stayed ahead in techs. Nothing really compares to just having more cities. A few awesome high level cities = weak. A ton of really crappy villages = unstoppable powerhouse. In the time it took the 3 AI's to settle half the map I settled the other half (medium size).

I think one very important ingredient is crushing growth quickly. Don't do it halfway; go all in. I do pick a couple early sites for conclaves and they will hit level 2 before I get growth crushed by city numbers. When you upgrade a village to a town it increases its zone of control. This is really bad if it expands over a lair. You want to be able to settle near lairs and place structures so that your zoc doesn't expand over them before you can clear them. So it's very helpful to consider growth in terms of how much time you have to clear those lairs and less growth means more time to do it.

As far as ratio I like 1-2 fortresses, 2-3 conclaves, the rest towns/villages. Fortress units are great but basic units from villages are still plenty useful in a pinch. For your last question I would take the 3/4/2. The best conclave buildings require a lot of production to build. Grain is almost irrelevant. Even with low growth you will end up with plenty of towns. With each one the faction food per grain just keeps piling up (because you're building the grocer chain). In my last game I wasn't paying much attention to food but I did notice at one point my faction food per grain was 390 iirc.

I used to run one major fortress (with X-3-2 or better), but the new city changes at L3 have been leading me to try two fortresses instead (one w Charge and one w Impulsive).  After that anything with 2 essence turns into a conclave, and stuff with 0-1 become towns.

I run 2 fortress (1 for troop - high mat/essence, 1 for unrest - high grain), towns on everything with 1 or less essence, conclave for everything else...

The unrest fortress allows you to tax high without worry, the troop one is self explanatory.

Prefered conclave yield is essence, then food over mat (you want it high level for the most research). Although this depends on the map size you play. If you're playing on really big maps with lots of cities, then mat might be better (because you'll end up with plenty of towns to generate food).

The towns is just there to help the empire grow and pay taxes, so it doesn't matter what they are on (although 3-4 grain is preferred).

2 grain really isn't worth settling unless it has 3 essence (mana/research outpost).