If you're lucky the Mongols will invade south of where you are, and face the Turks and Egyptians before ever reaching you. If you defend well, the Mongol warlords really aren't as tough as they make themselves out to be.
The ones you need to worry about when playing Russia will be the Timurids, by the time they invade, your realm will have expanded right there (they invade either just north or just south of the Caspian Sea). They come into play rather late though, so with if you handle quickly, with a swift war machine you can beat the campaign before they even show up.
I also think the Moors and the Egyptians have a very good starting position. When I played as Egypt I focussed on conquering westward and eventually crossing into Europe through Iberia. That way you don't have to be the first to deal with the Mongols. Let Turkey take the blow, and the crusaders that happen to be in the area.
DO+1 wrote:Their units really suck at the beginning ... and woodsmen
I have to disagree, woodsmen are among the best, if not the
best militia out there. They're only marginally more expensive than peasants, making them cheaper than your regular town militia, but with much higher attack, and great bonusses when fighting in the forests eastern Europe has so much of. They don't have the morale of some of the more professional units, but they more than make up for that in brute strength, and laughably cheap recruitment and upkeep costs. When you're just getting started, woodsmen are going to be what make your potential empire successful.