We have a concrete floor with linoleum tile. We will be leaving the tile in place. Should we glue the new engineered wood or put down a subfloor and nail the engineered wood into place? If a subfloor is the way to go, what type of plywood is recommended?
Either can be made to work, but both have challenges. Wood floor on slab is not a happy combination unless you prep the surface really well. And even then it has downsides, eg in winter the floor will be extremely cold. On the other hand, nailing the boards to a ply subfloor will give you great results, but you might have to fix every door, doorframe, base board, transition step and so on in the space to accommodate the raised height of the floor.
I would be confident that gluing to the slab can work really well, but much less so that gluing to linoleum would not eventually fail. Although it's an ugly job, stripping the lino off the floor would be my recommendation if you go this path.