For bases I used 3mm MDF hexagons. With a Proxxon rotary tool I created a cavity, to hot glue washers in, which will allow for magnetic storage.
Here you see the 'Mechs in various stages of construction.
I inserted a lot of pins to strengthen the joins. The LRM-20 on the Griffin I cut from a length of plastic tube. The basis for the LRM-2s on the Warhammer were two strips of wood, to which I added thin plastic card.