Recent Grad looking for help figuring out a plan for loan repayment and savings

Hello everyone! To start I want to say I am looking for any guidance on how much I should put towards my student loans, car payment, and towards savings.

I am a recent graduate (graduating this Sunday!) and am starting my first full time job on the 18th. I am payed hourly (30.50/hr, then 45.75/hr for hours over 40 per/w). I expect to work at least a full 40 hours every week with a high likelihood of overtime. Post tax/HSA/insurance/401k I would be making ~1,600 on a biweekly schedule (assuming I worked a full 40 hours each week). I plan on contributing $260 per pay period towards my HSA so I can max it out by December and am going to contribute at least 4% of my pay towards either a 401k or Roth plan.

I have a total of ~31,000 in federal student loans with an average interest rate of 5.8% ($338 minimum monthly payment, for 10 years). I also recently purchased a car for ~20,000 (with tax & 4 year total warranty included) on a 72 month loan at 6.29% (350 per/m). Beyond student loans and a car payment I have no other dept.

I am going to be living at home with my parents and commuting to work since I am required to travel frequently (anticipating at least 60% of the time out of office), so I will not have to pay any rent. I anticipate my gas, car insurance, and grocery expenses will be ~650 a month (my parents are having me help around the house by buying groceries instead of paying them rent). Beyond that I don't have any necessary expenses but would like to set aside at least 200 a month for fun things (eating out, gym memberships, movies, etc).

With paying minimum monthly payments on both my student/car loans, paying for other necessary expenses (car insurance, gas, etc), and setting aside 200 a month for myself my total monthly expenses are ~1,500 and I have ~1,700 left over.

I would like some guidance on what I should do with that extra 1,700 a month. My goals are to pay off my students loans as fast as possible, save up an emergency fund worth at least 3 months of my take home pay, save for a down payment on a home, and overall save towards retirement.

TLDR; recent grad with a monthly take home pay of at least 3,200/month with living expenses of 1,700/month looking for advice on how to save/pay off loans to meet my goals. Any advice on what to do is helpful!