Would that one work with any of these motherboards or should I go with the Intel Core i7-3770K
I would really like to have 32GB of RAM so is the one I selected right for the job, or is there a better one?
That's an Old Processor now, circa 2010... It won't work on any of today's boards. It uses the now outdated LGA1366 motherboards. If you want to spend fresh money on new products, I'd recommend today's i7 or i5 chips, these are much faster, and power efficient.
The i7 3770K is good, the 3570K is good too if you don't need 8 threads, and 4 is enough. They both overclock like crazy. Both of these are LGA1155 chips, and will work with any of the 3 gigabyte boards you mentioned. If you need that much ram, you will likely populate all 4 ram slots on your board.
You can pick and choose your ram of 32 GB kit from here: