I love this game. Very fun to play, easy and cheap to get into, and the tournament scene is filled with nice people who do a great job.
Best units depends on the kind of list you want to play. You'll get a long list of suggestions in this thread, and most are tournament-optimized lists. If you're playing casually with your gf, then really just buy what looks cool and try to weave them all together into a list. What you get will be fine.
Here are some expansion ideas (pick ONE).
For X vs TIE action, get a second box set, so both you and your GF each have the other game pieces. Then get one clamshell each of an X-wing and a TIE Fighter. That's five TIE fighters and three X-wings, which is a good basis for your squadrons.
Imperial players love TIE Interceptors, so Imperial Aces and a clamshell give you a total of three, which makes for a fine list.
Rebel Aces gives you a B-wing and an A-wing. Add a clamshell of each and you have two of each fighter.
If one of you want to go Scum and Villainy, then pick up the Most Wanted (Y wing and Z-95), plus three Rebel clamshells: the HWK, Y-wing, and Z-95. The minis can be used in rebel OR scum lists.
A large ship (millennium Falcon, YT-2400, JumpMaster5000, Lambda shuttle, V-49 Decimator, Slave One) is a great expansion. I've seen lots of X-wing+Millennium Falcon lists, and they do fine.
When you have a small collection, you field few ships with lots of upgrades. When you have a large collection, you can use swarms of low pilot skill, unupgraded ships.