Learning Oracle, does it matter if I install 10g or 11g? I'm taking a class in Databases, they're using Oracle 10g in class, but I'm having some trouble installing the database here in Windows 8 (auth problems), so I thought I'd attempt 11g.

Is 11g backwards compatible?

As in, just for learning, will I be able to not use the added 11g features?
Are you really trying to use Windows 8?  No version of Oracle is supported on Windows 8 yet and, if history is any guide, I wouldn't expect any of them to work without patches that aren't available yet.  Is Windows 8 even in public beta yet?  I'd hate to try to take a class using an early beta operating system.

Oracle 11.2 is supported on Windows 7 (which seems like a more realistic Windows version).  If you have Windows 7, that's realistically the version you need to install.  

What, exactly, does the class cover?  If you are learning how to do data modeling and to write basic SQL and PL/SQL, you should be fine using 11g since everything will be backwards compatible.  If, on the other hand, your instructor is teaching about database administration or is making heavy use of the Oracle Enterprise Manager (OEM) GUI, there are going to be a lot of visual differences that you'd have to compensate for across versions.  You can almost certainly get the same information from the 11g OEM GUI, it just may be in a slightly different place.