As probably one of the few here who's ever batch manufactured these here's my two pennorth. 12mm is not strong enough to withstand a good kicking, 15mm may be OK but is relatively uncommon thickness, so I'd plump for 18mm. The extra weight makes the object less moveable when the little dears decide to use it as a climbing frame. I used to dowel and glue construct which produced a square, rigid and extremely strong carcass well capable of withstanding racking motions, but failing that I'd biscuit joint. Avoid screws and pins/nails as far as possible as they can become a danger to children in the event of a breakage. Paints should be to the appropriate child-safe standard (search the site as I've put this in replies in the past) and lids require anti-slam or child-safe stays - try Ikea, Woodfit or Isaac Lord.
Scrit
Scrit