I guess, technically, to be able to use "everything", I would say go ahead and get one of everything to start. That way, you have a full set of every pilot card and upgrade. From there, you'll need to take a peek at how many unique pilots there are for each ship, and acquire the appropriate number of ships.
So once you have a copy of the Core Set, and one of each expansion ship, and thus have all the pilot cards, you would need to additionally get;
1 TIE Advanced
4 TIE Fighters
Now, the economical "next step" is make another Core Set purchase. You'll get another X-Wing and 2 TIE Fighters, but more usefully, extra dice that you will most definitely get better gameplay from. The extra templates and damage deck go to your opponent to smooth out more gameplay.
From there, I'd say make the final X-Wing purchase come from the expansion, so you get the extra non-unique cards.
I would also stick to the TIE Fighter expansions, rather than scoring a third Core Set, because those Swarm Tactics and Determination cards can be used by both factions easily, and expand your options that much more.
So, total shopping list, if you want a decent mix of options, and the ability to play all the unique pilots at once, if you felt so inclined, it buy 2 of everything.
It will be interesting, thematically, when the Millenium Falcon pack comes out. If there's are "Lando in Falcon" and "Han in Falcon" pilot cards, it a roundabout way, you're having cloned ships flying around in one match. I wonder if there will be a workaround, like the unique symbol goes on both "Han Solo" and "Millenium Falcon", so if you wanted a fleet of that ship, it would be the Falcon and some generics.
I think Slave I will be easier, as I can't see Boba Fett and Jango Fett both being represented, so it'll probably be Boba and 3 other "non-Slave I" pilots of Firespray ships.