I think you'll reach a point where Turf War will become stale. You'll want a ladder to climb and more stimulating challenges, and that's what Ranked mode is. Many Ranked players will only use Turf Wars as like a test playground for gear or weapons they want to take into Ranked eventually. I honestly just find Turf War to be a little too mindless to enjoy long-term.
At 13, no need to worry about whether you should be playing Ranked or Regular. Go at your own pace. Ranked will obviously be more testing and if you aren't ready to begin your ascent through the ranks, stick with Turf War until you're more prepared. Although, at C-, you really have nothing to lose so you can only improve. You might start feeling out the various Ranked modes and learning how to successfully play the objectives of each.
Thinking back, as an old-timer, Ranked was merely Splat Zones with 6 stages back when I started. For people starting now, there's a whole lot more to take in at once, so I'm sure it can feel daunting. If you have any questions along the way, though, don't hesitate to ask! Even if they seem basic or obvious.
As for Carbon or Aerospray, its been addressed, but in upper ranks Aerosprays become noticeably less viable (especially RG). Carbon is a common competitive weapon, arguably the best Roller in the game, so in the long run, it might be to your benefit to stick with upping your Carbon game early on. At the same time, you've got such a long road ahead of you, and so many other options to try out, I think its far too early to settle on a main. At your level I also used Aerospray RG a lot, and held onto it for a long time, but I reached a point where I wanted to branch out and see what all my possibilities are, and now I rarely use it. Splatoon has weapons to accomodate a ton of playstyles and strategic approaches. And how you play from now is bound to go through several drastic changes before you find what you're really comfortable with.
Good luck on your journey!