- I would like to write the code in the Arduino IDE environment, as I'm familiar with that (I self taught).
Ok. But if you do that, I don't know if the .hex files that you will get from the Arduino IDE will work on an AVR without the Arduino bootloader (I have never tried it).
- I would like to convert my UNO into an ISP. So I load the ArduinoISP sketch onto it, correct?
Yes. If you load the ArduinoISP sketch onto your UNO and wire it up like the instructions, you can use it as an ISP.
- Now, to get my compiled sketch on the second board, do I have to use what he used on that webpage (WINAVR) or is there a way to use the Arduino IDE to send the two files (main.hex & eep.hex) to the second board.
I don't know if you can use the Arduino program to flash .hex code with an ISP. I have never tried, but you can use avrdude which is free in all senses. It sounds like you can also use WinAVR (I have never used that program and am not familiar with it).
It would be really nice if you can just flash Arduino binarys directly to an AVR and have them work. The above post suggests that you can, which is good news.