I would like to build a small 10x10 fenced enclosure so I can put Max out on nice days. He likes to play with the adjoining neighbors dog and I can connect right to that fence.

For the ground cover, I would prefer to avoid concrete, but I want him to be clean and comfortable.
Is pea stone or river rock a good option? Maybe some pavers in the mix?

I had 6' x 20' runs for my dogs. Concrete. Easy to clean and it keeps their nails trimmed. Pavers would have the same effect. I read the 6' x 20' run allows the dog a bit more room to open up their stride. My dogs were perfectly happy and healthy in them.

I had Mason Kennel fencing that was first class at the time.

Concrete first choice, packed crusher run second.

If you have the space, I would make the kennel larger. I would buy a 100' of 6' high Red Brand horse fence and 1 10' by 6' high chainlink, kennel panel and make the kennel 10' wide by 45' long. Long kennels encourage the dogs to run more and keep them in better shape.

Put an apron on the ground of horse fence or cattle panels, attached to the sides. Bury the apron with the river rock. The apron will keep your dog from digging out.

Leave the top of the horse fence fairly loose. This makes it harder for a dog to climb out at a corner.

Make sure there is shade.

Back when I was training dogs semi-professionally, I had 12 kennels like this

Keith