To merge all of the objects together into one, you could select them, and use CTRL+J to join them all together. If you want to be able to select the vertices of each object from a dropdown, before you join them make vertex groups for each mesh. Select an objexct, click “new” below vertex groups. Name it whatever you want (it has to be a different name from the other objects’ groups. You don’t want naming conflicts). Then select all the vertices of the mesh, and click “assign.” You can do this to all of your objects. When you join them now, all the different meshes you joined should be selectable with the drop down list of vertex groups. Just select a group and click “select.”
Though if it were me, depending on the complexity, I would just join all the objects and use select linked using “l”. You don’t get a drop down that way, but when you select a floating mesh, it will select all the verts connected to it.