There are many processors from which to choose. Since you have selected a board already, you are limited to what the board's socket supports, and what the gigabyte BIOS supports:
Since there are several models of this board, I have picked one AS AN EXAMPLE: http://www.gigabyte.com/products/product-page.aspx?pid=5671#
In that link, gigabyte shows you the processors they support for socket LGA1151.
You may also use ARK | Processor Feature Filter to find processors, but you MUST make certain that the processor is SOCKET and BIOS compatible.
This message was posted on behalf of Intel Corporation
Thanks Al Hill, Afirsttimebuilder here you can find the comparison of all Intel® Processors in the list of supported CPUs according to the model you mentioned.
Hope this helps you.