Grumpy_Mike:
I'm new to the wiring/electronics part of arduino,
So you will find that the MAX6675 is quite good value for money. You need to amplify the signal using operational amplifiers. With such a low voltage signal these need to be very good operational amplifiers. They have to be carefully designed and even more carefully constructed. No doubt other might suggest a circuit but my advice is that it is a lot quicker, and cheaper and you get better results using the MAX6675.
I have the 6675 breakout board from adafruit. It works great.
I plan on making a bunch of these, and $12 per unit extra starts to add up. There are other reasons too (the 6675 does not support R or S type TCs...a software version could easily do so)
I realize I might lose some accuracy by going this route, which I think I can mitigate by averaging multiple readings. For my purposes, 5 degrees F of resolution is acceptable.
So, I would hope someone can point me in the right direction to amplify the signal as cleanly as possible.