Lots of great advice. Coming onto this forums has to be the best start.
Rallyarmor mud flaps. They're larger than stock and provide much better coverage against rocks/mud etc from hitting your paint. Subarus worldwide go with these on their rally cars.
Like previously mentioned : If you're not familiar with a skid plate, it's a large thick aluminum plate or "shield" that prevents your oil pan and other engine/transmisison bits from being severely damaged while offroading. It doesn't mean you're indestructible, so you'l have to be careful when you do offroad, of course, but it's a MUST if you plan to go off the beaten trail.
Lighting! IF you're going through dark streets, or offroading a little later in the day, you can look up quite a few threads here where people put up lighting bars etc to get some enhanced lighting.
Change your fluids! If you don't know when the last time they've been changed, or if the previous owners don't either (mom and dad possibly?) then you should considder it time to change those fluids! (brake, engine oil, transmission and/or differential fluid, engine coolant).
Filters: fuel filter mostly
Bushings: If you think your ride is too squishy, or you have a higher mileage vehicle, Subaru Forester and most Subaru Impreza bushings are all interchangeable.. You could upgrade to Kartboy, TIC(Turn In Concepts) or other polyeuthothane type bushings for added stability.
In fact, if you have a 5 speed manual, I'd strongly suggest changing out your bushings related to your shifter asap as those seem to be very flimsy in OEM form from Subaru.
Tires for sure. If you're on a lower budget, and cannot afford seperate sets of summer and winter tires, which are recommended for sure, you can still do some research and find an all terrain/all season tire that meets your needs. With research, you can find the best bang for your buck.
Welcome to the forums!
Oh, and take it from someone who had a nice headunit , fronts, mids, rears and subwoofers/amps in a vehicle before. Get a two-way alarm system that will alert you when your car is being broken into. Unless you declare and make sure that your audio equipment is covered under your insurance, your insurance company may not cover that part of your claim should that happen. I know I was out quite a bit of money since I only had fire and liability when I lowered my insurance to get into a new car..

Lesson learned.