As a new grad student, should I put Masters or PhD on my resume?
To a first-order, you should say what is actually true. If you enrolled into a Master's program and that's the program you are in now, you should not try to indicate you are really a PhD student. 

Past that, though, how exactly you state something which is otherwise true - how specific versus how vague, for instance - is a reflection of what you are using your resume or CV to actually do. If you are applying for an employment position, you should understand there is no such thing as a singular "resume/CV" - but a variety of versions which are all true, but emphasize different things and are more/less clear about some things, depending on the desired position. You are trying to tell useful story, and what's useful to someone hiring a staff researcher vs. an entry-level technician can be very different things. 

Sometimes you'll want to be specific, such as when your education is a very specific and useful fit for the position, where'd you'd say something like, "I earned my Masters's in Basket Weaving and am currently working on my PhD in the sub-field of Applied Stained Wicker Fabrication Techniques." In a job where the details aren't so relevant, to save space you might just say "I'm a graduate student in commercial art."

But to reiterate, the reality of your program at your school is important to what you say. If your program has 2 years of coursework that is like a Master's program, but they have not explicitly granted you a Master's degree (you could not ask them for a physical copy of it because they haven't granted you one), then do not imply or say you have a Master's degree. If your program is for a Master's degree and then they technically choose or allow students to continue on to a PhD program, don't just say you are in a PhD program if you aren't. Other than for general reasons of honesty, you'd be one question away from needing to say something like, "well, technically..." and then you'll have to back-track and look like you could just be making up everything you've said.