I think that UMass has the option to do a "qualifying paper," but it doesn't seem to be encouraged. I'm currently in a non-thesis requiring program, and while I'm not sure how that looks to admissions committees, it certainly limits opportunity for specialization at the MA level. Working on a thesis would give you the opportunity to show something off to PhD programs, and also to have a paper in your back pocket for presenting at conferences and doing the other things helpful to getting into PhD programs. At a program that requires a thesis, there is probably more funding available for travel and research than at a school where the thesis is optional or discouraged.
Given the schools that you're interested in applying to for your PhD, it would make sense for you to consider the CUNY schools seriously-- you could get to know the faculty at those schools, take or audit classes at them, and potentially have internal recommendations which go a long way. It's also likely that some of the other schools would fund you after the first year or semester.
Don't choose a school simply because of funding if it isn't where you want to be; I did that and found myself very unhappy with the decision. Of course, if the school where the funding is IS where you want to be, you're in doubly good shape.
Good luck!