I just finished a LONG campaign as the Hungarians. It was a lot of fun at first, but after a while, it really became a mad dash just to hear the victory speech.

If you're starting in early, you should be able to take most of the steppes and develop them long before the Horde arrives. The Horde comes in 1230. Have a nice welcoming party together of Halberdiers, Chivilric spears, LOTS of missile units (pavise x-bow, arbs, pavise arbs), maybe a couple of chase units (like knights or steppe heavy cavalry). The great thing about the Hungarians is they get some awesome generals. I couldn't remember where the horde arrives, so I built 7 armies for each of the 7 steppe provinces and spent literally 3 days battling it out in Khazar, Muscovy and Georgia. With 6 & 7 star generals, your missile troops get pretty accurate. Just don't forget to build as much moral boost as you can in your Halb provinces.

None of this answers your initial question though, getting started against the Byz. Well, I hate to break this to you, but your early position isn't strong. Luckily, the Byz have enough enemies you can fly under their radar for a while. Katank would tell you to blitz into every province you can, but I didn't even take Venice. I like to role play, so I made early peace with the Italians, the Poles and the Byz. I tried to with the HRE, but they wouldn't. They attacked Hungary from Austria and Poland/Italy kicked their ass on my behalf. This leaves you to focus on some very rich provinces out East. Get to Khazar as quick as you can and try to stay off of everyone's list. Remember, people don't trade with you if you're at war with them, so until you've got enough cash, focus on that trade empire.