Hi SOCAL! Here's my 2 cents if you're interested.
I would definitely list your EMT-B experience. It shows you have prior knowledge of emergency situations and assessment skills. I would only recommend becoming a Paramedic if you are going spend some years getting the experience under your belt. Without the experience, those in EMS refer to it as a "Paper Medic". Since you stated your goal is to become an ER nurse, go to nursing school and advance your goal that way. Although ER nurses and Paramedics are in the same area of emergency medicine, they are different.
I was a firefighter/paramedic for some time before becoming a nurse. I could not get into the ER even with 9 years of 911 experience. I was able to get hired in the IICU/PCU area (which I thought was strange). I finally got hired in the ER after 2 years of critical care experience. My Paramedic license helped me personally with IV starts, assessment skills, medications, and reading EKGs, but it did not help me get a shoe in the ER. I found that they only counted hospital nursing as experience.
I know this is anecdotal, but considering my background, I would still advise to go the nursing route if you want to be an ER RN or go the Paramedic route if you want to be in EMS.
Best wishes to you and your future!