So much for the so-called credible sites.. at least you went to more than one, and realized it. many people stop at the first one, and never realize "whoops.. there might be a problem here".
Here's the trick... names DON'T always come from just one place (and there is no magic "first" ancestor, from who all the Ballards are descended). All of the above can be (partially) true. The only way is tracing your direct paternal lineage back to where he originated (not being sexist here, the name comes down that way 90% of the time).
So, if you are doing this for you, you need to trace your ancestry. If it is an assignment, smile sweetly, pick any one of them and turn it in. We are not fond of teachers who do this assignment (lots of them) because they obviously don't know enough about surnames to know why it does not work.
ps if one or more of the sites want to sell you something, that is another huge red flag. They will tell you whatever you want to hear.