It is hard / impossible on most tractors of that vintage to shift the high / low range when moving. I would start off in high range 1st gear (5th) and then work my way up to High range 4th gear (8th). I would leave the shuttle in forward. A little gear grinding is common, dont force it in, let it fall into gear with slight pressure. Downshifting is tricky and requires floating gears (something I suck at). My Massey 20C of similar vintage is a 6x6 transmission (shuttle and hi/low and 1-3). I am always driving it down the road to different properties. At high range 3rd gear (6th) clipping along at 22 mph it can get places quick. I run a gear until the tractor will not go any faster before shifting, otherwise it bogs the engine down too much. Don't dump the clutch let it out at a moderate pace. Hills are your bane, tractors do not like to climb them, I have found on my Massy if I leave the throttle all the way forward, when I hit 1000 RPM's I downshift but pause a half second for the engine to rev up. This lets me climb hills the most efficently. Worse case you stop and downshift into low and creep up them.
On backhoes without clutches and only torque converter transmissions you need to shift into neutral to shift gears. It is a different sort of challenging.
@Tx Jim has good advise for on road shifting.
The JD 310A Hi/4 is 16.4 mph. Backhoes will bounce bad when they hit a bump and can become uncontrollable. I would take it slow if your not use to how they bounce down the road. If you have a boom lock for the backhoe it helps reduce the bounce. If there is no boom lock its like riding a bucking bronco. I would encourage putting a seat belt on if you have one, in case it starts bucking. Its a lot easier to get a tractor under control when your still in the seat. Remember when making right hand turns that the hoe likes to swing out in the left lane. Other than that stay safe!
I have roaded backhoes up to 15 miles at a time. Traffic will hate you, the damn backhoe will try to buck you off, and your rump will remind you the rest of the day. Farm tractors are much more enjoyable to road, way less bucking. Have fun, and let us know how it goes.