Every bit of data is important "obscure parameters" are completely subjective, but if only 3 parameters were available I would use surface, 700mb, and 300mb analysis. Many if not most other parameters can be estimated from these 3 key parameters, can estimate: 500mb, 850mb, CAP, Instability, clearing/cloud cover, lift, vorticity advection, boundaries, moisture advection, divergence, sinking motion, shear, and storm motion can all be estimated from sfc, 700mb, and 300mb analysis parameters.
Simon