The best way to level up fast is to bet big! For example, if you bet 20 lines at $1 each, you will level up 20 points per spin. However, bet $5 for each of the 20 lines and you will get 100 points. Obviously you have greater risk, but it tends to balance out in the end.
Also, if you save up a lot of money you can go on Civil Treasure and bet x15, x20 or x25. You really should get at least one bonus, giving you a big boost.