How can I create an "invisible" transition between different flooring types?
Solid hardwood is a tough one because unlike the other materials, it expands and shrinks. Laminate and especially engineered hardwoods with a plywood core are much more stable, but they will still expand and shrink a little bit. Certainly more than tile!

I'm in the middle of installing plywood core engineered hardwood in my own house and I have tile transitions. Here's what I'm doing: I'm leaving a 1/2" gap between the tile and the engineered wood and putting grout-colored silicone caulk in it. That way any expansion or contraction of the wood won't cause it to buckle against a more inert material, but there's still a visually-pleasing material in that transition.