First, don't save anything in a tax sheltered vehicle. You will be paying so little tax that there will be essentially no benefit to making the contributions, and you'll pay tax when they come out. Tax free compounding for 40 years is terrific, but start that after you're earning more than a stipend.
Second, most people recommend having a month's expenses readily available for emergencies. For you, that would be $1500. If you put $100 a month aside, it will take over a year to have your emergency fund. It's easy to argue that you should pick a higher pace, so as to have your emergency money in place sooner. However, the "emergencies" usually cited are things like home repair, car repair, needing to replace your car, and so on. Since you are renting your home and don't have a car, these emergencies aren't going to happen to you. Ask yourself, if your home was destroyed, and you had to replace all your clothes and possessions (including furniture), how much would you need? (Keep in mind any insurance you have.) The only emergency expense I can't guess about is health costs, because I live in Canada. I would be tempted to tell you to get a credit card with a $2000 limit and consider that your emergency fund, just because grad student living is so tight to the bone (been there, and 25 years ago I had $1200 a month, so it must be harder for you now.)
If you do manage to save up $1500, and you've really been pinching to do that (walking instead of taking the bus, staying on campus hungry instead of popping out to buy food) let up on yourself when you hit the target. Delaying your graduation by a few months because you're not mentally sharp due to hunger or tiredness will be a far bigger economic hit than not having saved $200 a month for 2 or 3 years. The former is 3-6 months of your new salary, the latter 5-7K. You know what you're likely to earn when you graduate, right?