I too find this popup really annoying - I really wish they'd do something to improve the selection UI.
I've made suggestions previously such as showing all objects of the selected tile in the right-hand menu, but the main issue with that is there are two very different things you might want to select - creeps, which move, and static objects, which don't. If you select a creep you want the selection to stick with it as it moves.
Actually that's another thing that's annoying - if you want to select a creep as it moves you have to click on the tile it is moving to. If you click on the creep itself you often end up with a popup that just says "road" because the creep has moved away. The UI should really handle click events on the creeps themselves, not just tiles.
Selecting the highest priority object sounds like a good idea, I guess the main question is how to make the optional menu clear enough but not get in the way. This could also solve the problem of ramparts - if I click on my storage I just want the storage, I rarely care about the rampart protecting it. If it selected the storage by default but had a menu where you could select the rampart with a second click that would be much better.
I would suggest the priority should be: