While "ideal" is somewhat subjective, there is a tool designed for this purpose, a "meat masher" or "meat chopper" (names vary). This is a tool resembling a nylon spatula, but with a cross or star of blades aligned with the handle rather than a single blade angled off the end.
The tool is used by pressing and twisting it vertically into the ground meat (or ...
I haven't cooked beef for a while, but a wooden spatula works very well, as it can break up clumps and is safe for non stick. I prefer the straight shape of the one I've got to any of my nylon spatulas, that are more designed for lifting.
The second implement matters less, but I may use a slotted nylon spoon so it's ready to lift the meat out of the fat, or ...
No, use whatever tool you have on hand that works.
If you use a teflon (or other non-stick) pan, maybe try to use something that will not scratch the surface.
Anecdotal, I've used everything, wood, silicon, metal, "plastic" , wood thingies (like the epicurean kitchen tools)