Three different beasts there.
Traditionally from my understanding trolling will be stiff and consistent all the way through the blank, jigging rod will will be soft tipped and progressively stiffen up closer to the handle, and a popping rod will be similar to the jigging rod, but I believe even softer in the last third towards the tip.
I have seen guys are starting to custom wrap parabolic trolling rods, which might be able todo triple duty if the blanks come long enough, but may just break the bank.
For an all around rod, I picked up a star boat rod thats 7' and has my 10k saragosa on it. Not ideal, or cheap but can get the job done, although not as effectively as a designated rod, as I'm sure action is being hindered with it.