Welcome! I'm on the same page with my car, I'm not looking to go too crazy since it's my DD and I wanna keep it livable/comfortable.
Just a head's up, everyone's gonna say "get a tune!" It's... it's the thing to do. I wouldn't say it's cheap, especially if you go past stage 1, since at that point you have to start replacing hardware, too.
That being said, your first step should be to check on some common issues these cars can have. Fortunately with a '13 you're safe from the biggest one, the engine-killing timing chain tensioner failure (the part was revised during the 2012 model year). A few others to be aware of, though:
-Bad PCV causing rear main seal to leak
-Excessive carbon build-up in intake manifold/valves (side effect of direct injection)
-Water pump. I think this was mostly just on the early years, like '10-11, someone correct me if I'm wrong.
-Suspension subframe shifting, both front and rear, due to loose tolerances from the factory. Pretty easy fix, and there are kits available at various price points. I'd recommend doing it even if you don't notice any shifting.
Manual or DSG?
Oh, if you didn't know, it's got fake engine noise. You can disable it in five minutes with zero tools (reversible). Google "mk6 soundaktor delete" if you're interested.