Marco, It is not bad to sing only a tenor range, it's better then only singing baritone these days, but it would be helpful to develop your lower register. It balances it out. And in a very rangy songs, you'll be asked to sing low notes as well.
Dreamcatcher, I don't know how old you are or where you live or what teachers are available to you. The current sound on broadway is that of Sutton Foster, high mix belt. It is not full voice Merman anymore. All the girls do pretty much the same technique. It is a mix that sounds like a very convincing belt. ex: Suttin Foster, Kerry Butler, Kristen Chenoweth (when she belts), Idina is mixing those high notes in defying gravity. The trick though is that they don't sound like they're mixing. If you're young and don't live in a big city, I would say that you should find a teacher who will encourge you, not get you paranoid about your voice, not get you too stiff or heady with technique. You want an easy free open sound. If your question is about whether to study classical or not, I say it depends how old you are, if you have time to study classically, that's a great base, but if you're about to move to NY or audition for schools, I would find someone who does more of a broadway thing.
She's tall enough to be your mother