6 months of all of your expenses in a high yield savings is number one. Good times are great, take it from me though, tomorrow they can stop and you'll be back to zero income, when that happens you'll be happy you have that savings.
After that, investing. Very easy to get into, if you don't want to get in right now you can just put the money in CDs and then swap it over to the market later. Not individual stocks, I'm talking index funds and ETFs, things that track the overall market, not a specific company. Then just set it and forget it. Don't check it daily or weekly, just let it sit and make you more money.
Treat investing as just another expense, that has the lowest priority. As Warren Buffet says, pay yourself first. So first pay your bills, then your savings, then with what ever is left as the other commenters said, set aside X amount for fun play money (and it's good to have a number for this, that number can spiral if you don't control it, all of a sudden you just spent 2 grand on a GPU you didn't need), and then put in your Y amount into investing. When times are good it is good to set everything you can for the future. You'll be happy when times aren't so good.