When writing about past research should I use the species name they employed or the modern version?
3. is right thing to do. You can mention in the introduction that "Campylobacter fetus, which was previously known as Vibrio fetus [Ref] ........."

You should not use the old name anywhere again (also for the sake of consistency), once you have made it clear that the species was renamed, in the Introduction. 

I don't think there is any written convention like that (As such usage of any obsoleted terms is to be avoided and the standard nomenclature as described by ICZN/ICBN etc should be used).