Hi Gailene, I started this discussion with hopes of others jumping in.
As far as the many different types? I certainly can't name them all :-)
Many different cultures and religions have used some form of meditation since forever and it is my understanding that most of them are trying to achieve a couple of primary goals. By quieting the mind and/or ego, you attempt to make a connection with your own true inner being, and/or your conception of some higher power.
Its funny I say that, when I recently started doing it again because I read that it can help me stay focused at work and that was the primary reason!!! But when I started doing it I felt deep inside that help with my focus at work is just one wonderful side affect that I can use this simple tool to help me grow emotionally and spiritually.
There are two types that I am working on at the moment:
a) Loving Kindness Meditation - which I just started
b) simple breath counting - which is what I use as a practice of quieting my mind and just being
There is a wealth of information around as far as the different types, checkout this wiki entry:
Good luck and keep us posted with your experience!!!
- Much Peace and Love