Jen, Don't be afraid, dancing is supposed to be fun!! It depends on where you're taking classes and what type (group or private), but beginning classes should ideally teach you the basics of the dance, at least one new step, and practice time.
Partner? What's a partner? If you have someone to go to classes with, great. Usually in group classes you'll pair up with person across the way and then switch--it's better to practice with lots of different leads. And don't freak out if you have to dance with a female instructor--it's like getting a mini private lesson.
Wear what's comfortable for you. Eventually you'll want to get dance shoes; they have a sueded sole that allows for easy turning. Heels or not is up to you--there are lots of choices. I myself feel like more of a "dancer" with heels. As for jeans, they're comfortable and hide a myriad of flaws, but you'll discover that they're usually WAY too hot to wear for dancing. Best best is a skirt; or light slacks or leggings with a tunic over it. There's a lot of mirrors in the studios--you'll discover what looks and feels best for you.
Good luck and keep dancing!
Alicia ;-p