We had one like that once.
We used cobblestone pavers, but first you should smooth the surface out really really well (you can even just use a rake if you put some time into it) and you should put down a perfectly even layer of sand underneath the pavers. Then when you have laid them out, you spread sand heavily all over them and use a broom to sweep it about until it's *packed* into the crevices. That keeps them from going anywhere. Ours held up pretty well for the year we lived there
We did the posts for crossties. They have to be set deep and in concrete. If you do the fence, I maybe would leave it on just two sides so two sides are open. That way if some kind of accident happens you or the horse have another option for exit without going through the fence.
Why not have the farrier or vet on it? Probably easier on the farrier to have a good surface
Rather expensive... but there is a product out there made and sold by Classic Equine (the most expensive barn stuff ever, LOL) but since it's for a small spot it might be reasonable.... It's cobblestones made of compressed rubber with traction on them. They looked quite nice and easy on the horses feet
I've also seen nice looking set-ups that are open on all sides and have a hitching post type rail going down the middle. Those are attractive.
You should also think about places for putting stuff. You don't want to have to bend over every time to pick each item up from the tack box on the ground. Then it gets tripped on, ect.
Don't forget to taper the sides from where the cobbles end. You don't want it eroding. I think you could use cobbles in a way to help that and also use some sand?
Also think of hooks for hanging bridles while get the horse ready. And think about the hose arrangement pretty hard. That can be so irritating, to have to drag a hose a gazillion feet every time to do your bathing/rinsing.
You might get some kind of faucet put in at the wash stall... then you could just hang a short hose right there... or even use one of those hose wand from above thingamajigs.
For ours, my mom actually did it as a project, and it worked pretty good, LOL! We dug a trench in a straight line from an outdoor faucet on our house, about 8 inches to a foot deep. Then we conjoined many many feet of PVC pipe so the whole thing was water proof... then we put a very long hose through the PVC pipe and laid that in the trench the whole way along. The hose attatched to the faucet at the house. Then we made a nice PVC contraption right at the wash rack, with the other hose end right there, and put a shorter hose on that. We had one of those valve things so we could keep the water on at the house end and turn it off at the wash rack.
What the pipe accomplished (it was a later addition and was very needed) was protected the hose from being stepped on, ridden over, bent up, kinked constantly, or driven over (we had to take our hay loads back there somehow, LOL). As well as making it available to bury the hose so it was completely out of the way and not unsightly. Best of all, no un-helpful family members could commision the hose for one of their outdoor projects.. they had to find their own, LOL!