I am a senior nursing student at a 4-year university...graduating in May! I am living proof that you can indeed survive nursing school haha
Anyway, I highly suggest working in a part-time/student position while you are in nursing school. If not right away, then definitely starting in the summer before your senior year and into your final year of school. I will say that the first year of a clinical program is a bit overwhelming, so you may want some time to get adjusted to your new hectic schedule. Maybe take the first semester or year off and once you are ready look for a CNA or EMT position (probably that summer). It will look great on your resumé and make you much more attractive to future employers.
As far as choosing between a CNA or EMT position, it really depends on your interests. If you have your heart set on emergency/critical care nursing then an EMT job will give you wonderful experience. But if you are looking for a more 'nursing skills'-oriented experience (should you decide to apply to other nursing specialties), then a CNA will definitely provide you with that. I think either way you are on the right track and future employers will be very impressed with your initiative for working toward both your CNA and EMT certifications. Especially in the current job market, we as new-grads must do everything we can if we want to be considered for positions against experienced RNs.
Kudos to you for being so driven and planning ahead. Best of luck in your nursing program...it will be a crazy couple of years, but so very rewarding! I promise