I think priority one would be to learn the difference between asphalt and concrete. Not to be smug or anything like that, but not knowing the difference could be an invitation for some contractor to sell you anything he wants. At least some knowledge of the problem is a good way to arm yourself.
I'm pretty sure you can tell the difference between concrete and asphalt if you just take a good look at it. You walk/drive/live on these surfaces all the time in daily life. If it turns out to be neither, then you have a real serious tennis court on your hands, probably built by real serious tennis players. If the court is only going to be for the kids & dogs, you may not need to do anything until you are ready to resell.