Just the core set is perfect to be played between you two.
One uses the Xwing, the other one uses two Tie Fighter (game is balanced so).
I suggest some games with just that configuration, to learn the rules and the game flows (let aside even the advanced rules plus squadrons rules).
Then you will be buying wave after wave in no time
(Actually I still prefer low numbers fights....they are MUCH faster, a bit more unpredictable, and I find them more fun than huge points squadrons fighting, but maybe it's just me).
EDIT: If you want to use all the ships you bought, yes...you need some more rebels ships to have similar points squadrons...but I still suggest you to start with the basic set ships (1 XW vs 2 Tie).