I just wanted to know what the max level you can get your profile up to. I'm a new player and I have no idea what it is.
You can level up your profile to 30. Once you are 30, it unlocks ranked play where it tracks your ELO (a numeric skill level).
What’s the new level cap?
There’s no level cap! Level to infinity (but not beyond it—it's dangerous to level beyond infinity).
Since patch 7.22 League of Legends summoner levels are no longer capped so the maximum will be constantly changing. You can currently see who has the highest summoner level here. However the in game champion level is still capped at 18 normally, an exception would be in URF games where champions can level up to 30.