If you want best price/performance, you can opt for an H110 or B150 (depending on the price and availability in your country), which are both designed to work with 6th-gen CPUs out-of-the-box.
The B250 motherboards supports both 6th-gen CPUs (such as your i5-6500) and 7th-gen CPUs out-of-the-box. So, if you are planning to get, in the future, a 7th-gen CPU without the hassle of updating the motherboard's BIOS, then the B250 will work.
There are no noticeable performance when comparing motherboards of the same chipsets. So between the Asus B250F and the Gigabyte Gaming B8, you should choose which number of ports/connectors and aesthetics/layout you need and like.
If you need 2x M.2 sockets, then get the Asus B250F; if you need just 1x M.2 socket, then either of the two will do.
If you need more USB3.0 rear panel ports, get the Gigabyte B8 as it has 2x USB3.1, 4x USB3.0, and 1x USB2.0 ports; the Asus B250F has 2x USB3.1, only 2x USB3.0, but 4x USB2.0 ports.
If you need more internal USB2.0 headers for front panel ports of your case or other devices, then get the Gigabyte as it has 2x; the Asus only has 1x internal USB2.0 header.
If you need more internal USB3.0 headers for front panel USB3.0 ports, then get the Asus as it has 2x; the Gigabyte only has 1x.
If you like the Black + Gray with RGB lighting look, then get the Asus; if you like Black + Green with RGB look, then get the Gigabyte.