I guess this depends on the type of research you want to do. If you're really into cutting-edge basic science research (like the stuff PhD's do), then Downstate isn't the best school for you. There is plenty of basic science research going on, but I don't hear much about it. However, if you want clinical research, then Downstate's great. There are so many opportunities for you to do research, even in competitive specialties like orthopedics, urology, dermatology, ENT, ophthalmology, etc. If you reach out to the faculty, they will find a project to put you on. There's also a research fellowship funded by the alumni association for Downstate students to do clinical, translational, or basic science research over the summer after M1 (I believe students get a little over $3000).
I find that the "limited research funding" isn't really an issue for medical students because most students go for clinical research projects that often don't require much funding anyway. The alumni association is also really helpful because they'll give students money to travel to present at conferences and that sort of thing. As with many things in any medical school, the opportunities are there--you just have to be proactive.