For shear simpleness it's hard to beat leaf springs. Fairly easy to set-up and have working.
Downside is lots of internal friction, making for a less compliant ride. If you like your eggs scrambled then that's not a problem. Ways to partly solve this are long leaves and extreme shackle angles. Both make for a lower effective spring rate which then will want shocks for control. Most common leaf sprung trailers intentionally use a short, stiff spring so that the trailer doesn't sway or need shocks.
One that gets thumbs down fairly often is rubber torsion. I don't have many rough miles on mine yet, but it's PO took it to Copper Canyon once and several Baja trips. Rides smoother than leaves, but this one (like the AT's) has RS9k shocks on it.
Coils are probably the best (excluding air springs from consideration), but to really take advantage of them you need to be competent enough to design and make or have made some sort of independent suspension system. Trailer suspensions are far easier than people carrier suspensions, but that isn't to say that they're easy.