Paying the student loan debt wouldn't be a priority for me, for reasons already mentioned.
To increase your credit score, you should have 3 credit cards. Two report a zero balance every month and the third reports less than 8.9% utilization. Alternate which one reports a balance. That doesn't mean you can't use them, but pay them off when due, so they report correctly to the credit bureaus. There is also a FICO boost when you have 5 cards, but only after you've had them for 2 years. Only let a balance report on 1/3 of them, and only less than 8.9% utilization (for optimal credit scoring). (Avoid store cards. Get real cards)
You would also need an installment loan, but your student loan counts for that. When you pay that off, you need to carry at least one installment loan to have a "mix of credit" on your credit report.
If you have anything negative on your report, message me. I may be able to tell you how to address it.
Time is your friend. You're young and can really set yourself up for success!