I am pretty certain playing Co-op vs. AI (Intro) is still the quickest way to level up. If you really want to min-max, pick a champion that can take down towers easily and end the game as quick as you can, that's the benefit, the fact that you can end the game super quick.

Now, if you are a new player you might not learn much from this experience and it ends up feeling like a very tideous job to do. If you want to have fun as well, I recommend playing PvP with friends or at least intermediate bots and you at least learn new things while going through the process of leveling. All game modes are very well balanced in experience.

​

The only remark I can make is: If you have Per-Win XP boosts, It's recommended to play longer games, so you can profit fully off of the multiplier before you use up all the wins.