NER: Extracting entities from an article
CRF is a standard for such case but bi-LSTM + CRF are said to be even better (e.g. https://arxiv.org/pdf/1508.01991.pdf). Not sure if you need POS as this is usually solved using the same techniques - may not help in the main task of entity extraction.

Depending how different are articles in specific categories and how much data you have for each of them, you may need to train each category separately and have some classifier in the beginning to decide category - like in your point 1. but word2vec-like classifier may be more robust here.