I have never tried linoleum, I would be concerned that (as you mention) it is too soft.
You could use 2x4's (I have), but I would limit it to where it is necessary for strength.
Here is one that is 6.5x2.5x3, which is completely the simple box concept, all plywood and FRP. I have had probably a lot more than 800 lbs of dirt in it without problems (except the wheels needed to be replaced with heavier duty ones).

The sliding doors on all except the oak are just windows from Home Depot mounted backwards, there are two things I would think about if you want to go with sliding doors or windows
1) Get windows / sliders with actual wheels, the teflon strips do not glide near as well and you will be sorry. The large glass on the oak enclosure is 1/4" plate, and I got the tracks at a glass shop. They were not cheap, but I started with the cheap ones, and the window would not slide as smooth as I wanted (the glass is too heavy).
2) Give adequate depth for substrate, look at the enclosure above and compare it to the ones in the garage post earlier, I built this before I built those. 1 foot is not nearly enough, a 2 foot dam will allow deep substrate and the monitors will not be at eye level with the windows, which helps keep dirt out of the tracks, and I think the monitors feel more secure when they are not completely open to the world.
Now for some clarification. I am pretty anal about this stuff, so take what you want and ignore the rest.
Anything that seems really clever was a borrowed idea (mostly from two people I respect very much), so I cannot take any credit for it. The only thing that is mine and mine alone, is the color blue....
Oh well enough rambling for tonight.
--Robert