What do I need to start with AVR UC3 Microcontrollers?
Microcontrollers are available with a wide variety of capability and performance. If you're just starting out, it might be wise to begin with something simpler (like the tinyAVR series). Atmel makes evaluation kits (such as the EVK1101) which I would recommend when working with a specific microcontroller platform. Such kits allow you to fully explore the feature set of the product without having to hook up external support circuitry (as much).

As for programming, you have a number of options again. If you look at the UC3 Tools page at Atmel, various compatible programmers are listed, such as the AVR Dragon. You can also probably use third-party programmers such as the USB Tiny from Adafruit, but I haven't personally used it for UC3.

You can use Atmel Studio to write and debug your code, but you can also use any text editor (i.e. Notepad++) and AVRDude to compile (I recommend you get WinAVR).

Finally, to learn embedded C for microcontrollers, there are many resources online. There is a lot of good references to programming at AVRFreaks.net. If you're really new to programming, you should probably look at taking an introductory programming class (many community colleges offer this) and also at some books about the subject:


Embedded C Programming and the Atmel AVR
Make: AVR Programming: Learning to Write Software for Hardware