With an all clay bottom, I would add plenty of structure before introducing any fish. They need to have a place to live and breed as well as hide from predators.
Stock fathead minnows and nothing else the first year or two. Next, introduce yellow perch fingerlings and let them grow and reproduce. Lastly, Introduce walleye after the yellow perch are well established.
It will be interesting to see if the walleye will be able to reproduce in your stream. I assume you would need to add some gravel in the stream for that purpose.
Disclaimer: I have never tried the above approach; it seems it could work.
I bought a backhoe so may have to try a small walleye on yellow perch pond here.
