Take the rubber lip liners off of the quarters, if it still has them. That will prevent trapped moisture from rotting the seams very quickly.
Jack up the car, remove the rear wheels, and wash the insides of the fenderwells REALLY well, especially the lips of the quarters. Scrub the snot out of the areas that rust, because that's where dirt and debris likes to settle and trap moisture against the sheetmetal.
If you live in a place where it rains frequently, or drive this car through the winter, the next best step you can take is to coat the inside of the quarter panel, the quarter panel lips, and even a little of the flat area on the outside of the lip with some quality chassis paint. Prep the area by scuffing the inside with a Scotchbrite pad, then clean it with some Wax & Grease remover so the paint adheres well. There are lots of options to use here, but see what you can get locally.
Stay away from Rustoleum.
I've had AWESOME luck with Chassis Saver paint- it's incredibly durable and does a great job of sealing out moisture. It comes in a half-pint can like this:
Jegs carries it, so does Amazon; but I got it cheapest at a local Auto Body supply store locally.
This is what the underside of my 2015 WRX looked like before it's first winter here in NY. What you see is actually what's covered by the factory plastic splash guards and skid plates, but I
REALLY didn't want any rust to even get the chance to start! The paint has held up incredibly well, and none of the usual "surface rust" has appeared where most people get it already.
Congrats on finding a low-mile, clean 4th gen!
