Hi! I was in a very similar situation to you when I started grad school four years ago -- similar amount of debt (although most of my loans were subsidized), and a desire to start paying so that I didn't accrue interest well into my mid-30's.
I will assume your stipend allows you to meet basic costs of living and perhaps even have a small emergency fund. If that's the case, I encourage starting to repay -- I'm so glad I have the past few years! I make a monthly payment of around $300, which disperses across my federal loans. Loan servicers generally consolidate all student loans into a single monthly payment.
Once you begin repaying loans, you can (and should) set up a monthly automatic payment, which deducts directly from your bank account. Do this. Don't ever think of that $300 (or whatever your payment amount is) as part of your negotiable monthly budget -- the money is just not yours. I believe you can often choose your monthly payment date, so you might consider having them draw your loan payment from your account a day or two after your paycheck comes, so you only see the money in your account for a day or two before it disappears. You could also open a checking account specifically for loan payments, and just always make sure you have your monthly payment in there ready to go. My loan servicer (Mohela) notifies me a few days in advance of drawing a payment, and notifies me when they've taken it as well.
First step -- contact your loan servicer and try to talk to someone about entering repayment. What would it look like? How much would your monthly payment be?
I still don't have a target date for repaying all of my loans-- I assume that's a decade or more off. I know I've paid down a few thousand during grad school though, so definitely made a dent. Perhaps one day I'll have a 'real' job and be able to make larger payments, but I'm fine with humming along!