The only default style you will see is the [Basic Paragraph] font. You can create new ones yourself, or import fonts from other documents using the Load Paragraph Styles, Load Character Styles, or Load all text styles commands from the styles panels' flyout menus.
No, InDesign does not come with prebuilt paragraph or character styles. To do so wouldn't make much sense since there are millions of possibilities.
Format a paragraph of text the way you like, then choose New Paragraph Style from the Paragraph Styles menu.
It sounds like you need some basic instruction in how to use InDesign. I highly recommend Sandee Cohen's book InDesign Visual QuickStart Guide. It's inexpensive and will save you tons of time. Here's a link to the latest version, but there are editions for all versions of InDesign: