Before I applied to grad school, I made sure I applied to institutions where there were at least 2 profs whose research I liked. Then I visited the schools where I was accepted. Many schools will give you a small stipend to visit (it's been many years now, so that may have changed). At one school I visited the students said, "DON'T COME HERE".
The teaching part can take up lots of your time, but check with the graduate school you are applying to. Many have only a 1 year teaching requirement. Larger institutions move you onto research stipends once your teaching requirement is met. Ask students when you visit or email them.
You might try visiting phds.org to do some of your research. Good luck.