Hmmm i try and avoid war with established powers aslong as possible, when i take modavia and kiev i have enough trade profit to keep me steady, theres no point conquering to much in the east because the mongols will ruin it for you anyway, waiting for a power to fall some might think is risky but odds are with you chances are either byzantium or the holy roman empire will be crushed or crippled with civil war thats when hungary can start to expand.

A strong byzantium can play in your favour as already mentioned letting them overstretch themselves on the steppes is a good thing for hungary but they can be a buffer state to the mongol horde and you might be able to get a peace treaty with them, stranger things have happened lol.

Whatever you do try your best to have lands some distance away from your homelands because its highly unlikely if the mongols decide they hate you lol which they probably will, that youll be unable to hold them off for long, some provinces far away atleast means you can fall back on something. With a strong navy sicily is always a very good target.