I am just beginning to learn how to use microcontrollers, and I have decided I am going to learn on the UC3B 32-bit avr. I will also be learning C programming in the process. What do I need in terms of programmers and other necessities, while staying pretty cheap, and where are some tutorials to help me get started?
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.
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:
Nice choice actually, been working on those things for the past months, both in the low power area and for general purpose, including USB and stuff like that.
If you've already decided on the B series (it actually doesn't matter, only few components change between the series such as the ADC) get the EVK1101 and a JTAGICE3. That's it, nothing else needed, no adapters, nothing. Plug both into USB and you're good to go (ok, you should download Atmel Studio).
First thing to note: Start with an already existing example (the ASF (framework) comes with many examples for nearly every component). Understand, which functions to execute.
Also, make sure you read the chapters on clocks and the power manager thoroughly.
This might not be the answer you're looking for but please consider this:
You might have a better learning experience starting out with the 8bit AVRs, also from Atmel. All of Atmel's MCU are supported by Atmel's IDE AVR Studio so you learn the IDE once and keep on using it when you move on to more powerful MCUs.
The IDE is fantastic, really got better with version 6 and comes with visual assist for free!!!
Regarding a debugger / programer. I would invest a little money and buy the JTAGICE MKII and avoid all 3rd party programmers and debuggers! When I started out I used a 3rd party programmer with AVRDude and all kind of 3rd party apps and wasted a lot of time setting up the environment just to get going. Save yourself the trouble, that extra $100 - $200 is worth so much less than your time. Of course the JTAGICE MKII also supports all the protocols Atmel MCUs use (JTAG, ISP, debugWire).
Your best source for anything Atmel - www.avrfreaks.net which is a developers and support community like no other.