Using Arduino to learn AVR programming
If your chips have a bootloader already installed in them, you can use any USB -> Serial cable (FTDI cable) to program them in-circuit on their Rx/Tx pins. If not, you can use the Uno to program a boot loader into them (one time) and program them with the cable from then on.

To use standard C, you can use the bare chips or the UNO. You'll want a different environment than the Arduino IDE, though. That can be anything from an editor, the the gnu compiler tools run from a command line, to almost any other IDE. A number of people, myself included, use the Eclipse IDE with an AVR plug-in and do almost everything from writing the code to programming the AVR from within it. (I say 'almost' only because I personally prefer a full-blown programming editor, run outside of the IDE, for initial creation of sizeable projects or major edits and rewrites. That isn't necessary, though).