I'm guessing everyone here will take an instant dislike to me when I admit that I've only seen "The Man Trap" and the two Abrams movies.
Nah, the fact that you show an interest in seeing more, actually lends credence to the fact that even though not everyone likes the new movies, we all have to accept that they are likely to bring new people to the fanbase
I'm a TNG fan myself, but you'd very likely want to check out the original series since you're already familiar with the characters, & you'll definitely want to view the cinematic films of the original cast, from back in the 80's. I can't say whether it's worth it to you to invest in the dvds or blurays, as it would be quite a large dollar amount. Certainly if it's available where you are, Netflix is the way to go.