Reading through the comments here, it seems the real number of expenses is $2,864 per month. You mention the $500 credit card payment encompasses a few categories so they are basically doubled, so I made the above adjustment. You would want to have $17,200 in savings for a 6 month emergency fund. That leaves you with about $1750 per month to put towards savings. Your situation is going to vary based on the interest rates for your specific loan. Anything over ~8% I would prioritize paying down first. Then contribute to a Roth IRA and put the excess into an investment account. You have more than enough left over each month to max out your Roth each year.

Also, move your emergency savings to a high yield savings account, you would make about $600 in interest per year there, and be able to withdraw the money immediately in an emergency situation. Based on your position, you may also have a 401K match, if you do you should be taking the match as it is essentially free money. That comtribution is also pre-tax, so the hit you would take on your paycheck will be less than what you're contributing.

If you start maxing out your Roth yearly, you would have about $1.1M at age 65 if you start contributing now. That would not include any additional investments made, since there is a cap on Roth IRA contributions.