Yes, go register. I think you can do that at the post office (?) Or if you live in a big city, at you local alderman's office. You have to bring proof of where you live. ID and/or phone bill, something like that.
The bottom line with republicans and democrats:
Republicans beleive in the trickle down effect: If you make the top rich people richer, the money will trickle down to everyone because the top guys will have big businesses where they can hire the other guys, and then the other guys will have jobs, etc. It's sort of "work hard and you'll get what you deserve."
Democrats beleive a little more that we have to watch out for the little guy. So yes, they may raise taxes, but then you get more services for the little guy like Head Start, or universal health care, etc.
Maybe you already know all this, but I just love introducing JWs to politics.
I personally am a democrat because I was raised poor, mental illness runs in my family (thus "getting a job with health insurance" is just not realistic for some of us), and I work in healthcare, so see the "little guys" who fall between the cracks. The're not lazy, they often do try to get a job, but it is just not possible for many people out there to live a perfect 9-5 life.
ANYWAY, you should register to vote, it's just one more step away from the JW mindset that you should follow your authorities, no questions asked.