Ice rod for hard water rookie

[Fossil Fish]

I've been on the fence about ice fishing but this past weekend a neighbor said he'd like to give it a try as well. That was probably all the motivation I need to do it, so now comes equipment buying time. What would be the ideal rod strength for multi-species ice fishing? Likely the main target would be perch, but if I had the stuff anyway, I'd give walleye, whitefish and lakers a try at some point too. Throw in the occasional pike while perching and it gets better. I'd guess a medium action rod -same as soft water, or would a medium -light suffice, or do perch on an ultra light (love that in the summer) and med-heavy for lakers. Thanks in advance