My recommendation would be to use Lépésenként magyarul 1/2. Although these books are intended for studying in a group (they're written in Hungarian and provide little explanation for grammar, thus leaving it to the teachers), combining them with a grammar book, audio material and a dictionary is a bingo. I have no idea what's TY Hungarian like, but according to my experiences with TY Finnish/Catalan, I wouldn't learn by it. Colloquial Hungarian is not a bad book for beginners, but I got bored after a while. Halló, itt Magyarország 1/2 is quite old now - the vocabulary is okay, but the texts and situations are prehistoric.
Hungarolingua is apparently okay, but I've never learned by it so I can't tell you my opinion on it. There is also a bilingual hu-eng grammar book called "Gyakorló magyar nyelvtan", very useful, lots of examples, explanations and exercises.
Good luck with your Hungarian!