Two core sets is a great way to start for a few reasons. First of all, a second core set is usually cheaper than buying three separate ship expansions. You also get more dice and tokens, plus an extra set of maneuver templates, which is helpful for playing with people who may not own the game themselves.
A thing to be aware of is that the two core sets have different damage decks. The original one was updated and included in the Force Awakens core set to address some balance issues (namely some of the critical hit cards having no effect on certain ships and builds). Either deck is usable, but be aware that there are differences between the two. The Force Awakens deck has a small "1/33", "2/33", etc. in the bottom left corner of the card so you can tell the sets apart.
For more advice, I'll point you to the X-Wing forums
here on BGG. More veteran X-Wing players will see your questions there and you'll get a lot more help.