Yay, new Filia player! :D
I play Filia quite a lot, as she's on the the second position of my main team. Though Im not too great at the game yet, maybe late beginner or early intermediate.
Filia is a really nice rushdown character, like you said, so make use of that. A lot of her combos can be a little tricky with the timing, but the one that's good for teaching the framework of a lot of her combos would probably be similar to the
final one from the Air Combos tutorial.
Usually, when I play, I try to start with jump-ins (j.HP ftw), but usually only against characters that I can easily get close to. With zoning characters like Peacock, or to a lesser extent, Parasoul, I make use of her hairballs in the air to get closer, or to try getting close enough to catch them with a H Ringlet Spike. Opponent keeps jumping? Meet them in the air and throw them, or catch them with Updo/Fenrir. Running away? Use airballs and air dashes. Spamming pokes? Use a sweep or grab them.
With a beginner Filia (or really any character in general), I would advise to stay within your skill range. While attempting a flashy 10k 3 meter counterhit combo right off the bat might seem tempting (if you want to, do so in training mode), a lot of Filia's attacks are very unsafe on block if you drop the combo (sHK and H Hairball being notable offenders). Master shorter, more practical combos, and gradually lengthen and optimize them as you play.
About her supers, Gregor Samson is really,
really good for chaining combos off of. Even a simple string like
c.LK c.MK s.HP j.LP j.LK j.MK xx Hairball can be chained into Gregor to make for a nice lengthy, damaging combo. It also makes for a really good punish.
Fenrir Drive is my go-to combo ender. I use it a lot more frequently than Gregor, tbh. Outside of the end of combos, Fenrir can also catch unblocking airborne opponents. If it's used facing the corner, it'll keep your opponent there. If the opponent doesn't tech, you can OTG off of it as well.
Tricobezoar is less used on my part (mostly because of me not saving up for it), but it has nice damage (albeit kinda difficult to combo into). A well-timed Updo can get your opponent into the air so you can use Tricobezoar. I also use it to catch any stray gliding Bellas.
Beginner Combo
s.LK s.MK s.HP j.HP j.HK
c.LK c.MK s.HP j.LP j.LP j.LK j.MK xx Hairball
(end with Gregor after Hairball if you want to continue combo)
(intermediate?) Combo (Midscreen)
c.LK c.MK s.HP j.HP j.HK
c.MK s.HP j.MK xx H Hairball ADC j.MP j.HK
s.LK s.MP c.MK xx H Hairball -> Fenrir
~ 6.8k
(intermediate?) Combo (Corner)
s.LK s.MK s.HP j.HP j.HK xx H Hairball ADC -> j.MP
s.LK s.MP c.MK s.HK xx H Hairball
c.LP s.MK s.HK xx H Hairball -> Fenrir
~ 7.4k
Good Luck learning Filia!