To put 1" (loose) of gravel on 300' of road @ 8' wide, would take 7 1/2 cu yds. That's really not much at all. I am a gravel contractor in Canada. I would recommend having 20 yd spread on it in 2 passes - likely in & out, with about a 3' overlap in the center - to build up the crown. Then don't hesitate to add 10 yd yearly for the next 3 years. After that you can likely cut back to every 2nd or 3rd year. Maybe a small pile in your yard that you can dig into with your FEL to fix up any trouble spots might be a very good idea too.
As far as what size of gravel to get...3/4" or 1" maximum size. crushed gravel preferrably, as the rough crushed edges tend to lock the stones into place. Round material tends to shift around. Stay away from 'pit-run' gravel....unless it is 2" or smaller, the big, round stones are even worse than small ones.
You may want to look into finding some larger 'rip-rap' stone (4 to 6") to place across your new ditch to slow the flow of the water running down it. or even a few straw bales if you have access to them. This will give a chance for some vegetation to grow and stop the erosion.