Wired or Wireless is not the question...its much deeper than that...you need to get to know your mouse...delve into it’s subconscious...figure out its inner workings...find out who your mouse is or perhaps trying to be in it's own mind...once you've done that....only then you can make a proper decision...i recommend staying away from any aspects or character defects you may find that pertain to the following mice…
Chuck-E-Cheese, Mickey Mouse (or Minnie b/c every 28 days or so you'll be the problem, not her), Fievel Mouskewitz, Jerry, Monterey Jack, Mouser, Pinky or The Brain, Danger Mouse, Itchy, and especially not Speedy Gonzales or any of the Three Blind Mice.
Instead I would lean more towards these fine rodent examples….
Stuart Little, Master Splinter (Probably the only rat you would want to check out, I would be leery about straying from the mouse breed, rats and hamsters have been known to be quite problematic), and of course the obvious favorite Mighty Mouse.