I've had quite a nice game as the teutonic order (XL; High). they start out in livonia which is nicely upgraded but also dirt poor...you're neighbouring two one-province factions which are richer than you and which are rather unassailable at the beginning. esp the lithuanians turned out to be extremely aggressive but soon faced war with all bordering factions so they were a mere straw fire.
the main problem is that there are no attractive territories in your immediate grasp. estonia is unruly and even poorer than livonia, even though it provides interesting auxilia cav; novgorod is too well defended most of the time (those damn boyars!) and the lithuanians spawn 6- and 7-star-princes like hell....
another issue I noticed is that the princes' quality seems to depend on the king's influence among other things. since this rating is likely to be rather low most of the times, it is an ansolute priority to train at least one unit every turn in order to get those generals appearing at certain dates. once I read them all somewhere for vanilla MTW but haven't found a list for XL since....is there any?
In the end I found conquering Scandinavia the most satisfying option, also a difficult one though. it provides a better strategic position against the horde (well, a little haven at least provided you rule the seas), you'll have to deal with the swedes and the danish, though, which isn't likely to improve your reputation with the pope. once scandinavia is conquered and the baltic sea is under control, get the sea trade going. you won't have any cash otherwise, and even though the order units are among the best in the game, the horde will prove to be a respectable challenge to them. I played rather defensively so when the mongols finally reached me in ~1270 (they must have loitered quite a while) I just owned the provinces surrounding the baltic sea and was almost overthrown by their onslaught when they hit me in lithuania and novgorod. you can only win so many battles when outnumbered 4:1....I held them off (that forest on the lithuania battle map must be filled to the brim with corpses by now) but was deeply in the red afterwards thanks to some emergency bribes.....try them, it's tough but it's fun. having teutonic knights for family cavalry is simply GREAT!