Text-Classification-Problem: Is Word2Vec/NN the best approach?
1) Max-Entropy(Logistic Regression) on TFIDF vectors is a good starting point for many NLP classification task.

2) Word2vec is definitely something worth trying and comparing to model 1. I would suggest using the Doc2Vec flavor for looking at sentences/paragraphs.

Quoc Le and Tomas Mikolov. Distributed Representations of Sentences and Documents. http://arxiv.org/pdf/1405.4053v2.pdf

Gensim(python) has a nice Doc2vec model.