The H310 mobo can support the I3-9100F but the problem is that it surely need an update of the bios to support it. For example, the "Asus prime H310M-D" needs the Bios 1404 version to support the I3-9100F.
This means that you need to have a cpu of the eighth generation that works with any version of the bios or alternatively that your provider updates the bios. In any case before buying a mobo make sure on the website of the manufacturer of the appropriate bios version.
For the price difference I would recommend that you look at the 8GB version of RX 580.
Anyway In 1080P you don't have to have any difficulty in the current games.