As he is not youngstock, bridle with reins over the head is correct turnout, no need for Inhand bridle,
As for tail, if you can plait if very neatly then you could get away with it. Pulling looks better, If you don't like the idea of pulling the tail you could use a tail rake to give the appearance of a pulled tail (I use a tail rake as Reeco would kill me if I pulled his tail)
This is me showing Reeco in an inhand class, he is turned out like a hunter so aim for this (replace the jods with trousers. I only wore jods as I'd left my trousers at home.