For Christmas I have received the TFA starter and Imperial Aces pack. My friend has the classic core set plus an X-wing and A-wing.
Can you recommend some good lists than can be made using these sets?
Also, what would you recommend buying next? For now, we're playing casually within a group of friends, so tournament meta doesn't really bother us.
For your friend I'd probably say the Falcon or Rebel aces since it seems like he's leaning towards the rebels. As for the imperial side; I'd probably get a VT-49 or the TIE interceptor expansion.
On the other hand; you could just buy what you like. If you're just playing casually then fly what you enjoy. 
As a new player myself, I prefer the squadron builder below. Once you input which sets you have it only gives you options that you currently own. Of course for your casual games you can proxy cards but this will help you with "tournament legal" lists as well as helping you figure out what you want/need to by next in order to get the ships or cards you want.
I'm not sure if you wanted to mix your collections or not, but I erred on the side of caution by assuming you'd be building separately.
Here's an Imperial list with your collection:
"Omega Ace" + Push the Limit (23)
"Epsilon Leader" (19)
Carnor Jax + Push the Limit + Shield Upgrade (33)
Turr Phennir (25)
TOTAL: 100
"Omega Ace" just flies right into range 1, uses Push the Limit to get a target lock and focus token, then spends both to get 3 critical hit results. Carnor Jax is a major target because his ability is so annoying. Try to keep him out of arc as much as possible.
For your friend:
Tycho Celchu + Homing Missiles + Push the Limit (34)
Wedge Antilles + Proton Torpedoes (33)
Biggs Darklighter + R2-D2 + Proton Torpedoes (33)
Wedge and Biggs go straight up the middle with Biggs guarding Wedge so that his awesome ability lasts longer. Tycho wants to flank the enemy. These ships all have ordnance (missiles and torpedoes). One thing you want to do with these kinds of weapons is not fire them until you have both the target lock and the focus. For the Proton Torpedoes, you must spend the target lock to fire them, so having a focus on hand to change extra eyes into hits is good. Granted, it's not as necessary with these since you do get one free eye to turn into a crit. In the case of Tycho's Homing Missiles, you don't spend the target lock which means you can use it to reroll dice, but getting the focus in the same turn shouldn't be hard since he has Push the Limit. Tycho can just take all the stress he wants and still perform actions, but he still has to watch out because he still can't perform red maneuvers when stressed.
For your friend I'd probably say the Falcon or Rebel aces since it seems like he's leaning towards the rebels. As for the imperial side; I'd probably get a VT-49 or the TIE interceptor expansion.
On the other hand; you could just buy what you like. If you're just playing casually then fly what you enjoy.
I'm thinking about the TIE Interceptor to have all the pilots, and after that we'll see. I was also thinking about getting Slave I because it looks fun to play and has the Stealth Device included, which will be useful for my Interceptors. I will probably want to play in tournaments, so I prefer to learn to play with what I have.
Z-95 Headhunter (I'd get two)
Y-Wing
E-Wing
TIE Advanced
TIE Bomber
TIE Interceptor