It all depends on you local requirements. Some areas require previous EMT experience some may not. In regards to going onward to Paramedic, that will depend upon your goals. Personally, I would not recommend it to someone that wants to do it as a hobby. It is far too hard, too long and the license/certification is difficult to maintain doing it occasionally. Remember most certifications require proficiency in areas, as well as continuing education, CPR, Advanced Cardiac Life Support, evidence from a licensed physician that you have maintained those skills & knowledge as a Paramedic. NREMT (don't believe MA is a state requires such) requires you to be working at your current level.
As well in regards to the physical, they may not state it but nearly all schools require some form of medical history, drug screening, and personal background checks before allowing students into the clinical portion. CPR for healthcare will either be taught or required before clinicals also.
Now, the bad news. EMS is a very, very contagious bug. Once it has bit you, it is very hard to remove the symptoms of it. I have known several that have quit their 6 figure salaried job, became divorced, moved across the nation or world all over this thing called EMS. So do not be surprised if it does bite you. I have forewarned you....
Good luck!
R/r911