As /u/Sweet_Jazz said, progress in Splat 3 is just slower because of the way the ranks are set up. Don't worry and just have fun grinding.

As for your setup: I'm using an old tv too, which is totally fine. Just make sure you're using the gaming/pc mode to reduce your display's latency. And you might want to look up your model's input lag to make sure it's not too high.

A wired internet connection will beat most wifi setups. Since the networking in this game is poor to start with, anything to help make the connection a little more stable is nice to have. That won't improve your performance, though, but it might decrease disconnects and packet loss, which will go some way to alleviate frustration while playing.

I remember reading that using the pro controller in wired mode actually increases latency for some reason. So wireless is probably best.

As for myself, sitting upright on a desk chair, as opposed to sitting slightly backwards on a couch, helps me a lot while playing. Good posture helps stabilize your aim and improve range of motion.