Watch some VODs (search tabletop simulator x-wing on youtube) or go to your LGS and watch people play factions. Pick one you like and buy one of the top archetypes for that faction on metawing. Usually that means buying a faction starter box, core set, and a few other ships which will run about $100.

The absolute cheapest way to get into the game would be to buy a discounted core set (even old edition), buy some used and common ships on ebay (they can go for about $10 a pop individually or even cheaper per ship if you buy someone's old collection), and then buy a conversion kit. The rebel alliance, galactic empire, and scum and villainy conversion kits have almost all the dials and cards you need to play every ship in their faction as long as you have some version of the ship on the board.

I sniped ships and conversion kits on ebay for basically half-off to get my 2nd and 3rd factions fairly cheaply but it can take some time to get everything.