There is really no way to offer an "average cost" or to estimate a cost, IMO. How do you want to build your panel? Do you want structural foam like CoreCell or cheap EPS? Do you want a soft top, fixed roof or lifting hard top?
Do you prioritize weight over heat/sound insulation or is ease of construction more important to you?
Phenolic is a bit of a misnomer, as phenolic is simply the resin in which the canvas, cotton or fiberglass cloth is soaked. A pre-formed phenolic sheet is kind of like "posterboard". Phenolic has been used for decades, as an insulator and to make products such as rotary dial phones, owned by the phone company, for those old enough to remember that.
The cloth can be woven and had in various weights. It is coated with phenolic resin and cured, often by heat and pressure. This creates a thin sheet that is flexible in one direction, but it easily punctured. It is quite heavy for its thickness, but has decent tensile strength. Carbon fiber and Aramid/Kevlar sheets are made in much the same way, except that epoxy resin is generally used instead.
Procuring pre-made fiberglass (Filon) sheets or Phenolic sheets (Dura-SIP) is not difficult, neither is adhering them to a sheet of EPS or XPS foam. You will not achieve the quality and performance of a commercial panel, which is likely pressed, vacuum bagged or cured/baked in some way.
Do you want a smooth finish like Gelcoat on a boat? How about a brushed aluminum or stainless steel for durability? Sheet metal can be bonded to foam just as easily as phenolic sheet can. Each has its advantages and disadvantages.
Are you building the box as one unit or do you want to build panels and screw or glue them together to make a box? This will change how the panels are constructed. A finished panel can be bonded to another panel using an extrusion or a simple 90 degree angle to offer some support and seal the joint. Once the box is completely assembled, it is quite rigid and strong. The stiffness or rigidity comes from the rigidity of the panels, which ironically comes from the combination of two or more very flexible sheet goods (cloth, phenolic, ABS plastic, sheet metal, XPS foam, etc.)
Will cabinets or furniture be built "into" the box or using the same materials? If the box is SIP and you are going to buy COTS cabinets from Home Depot, that changes construction plans, material quantity and costs.
If your focus is weight, go with thin skins and low density foam. The more air that is trapped in the foam, the less thermal conductivity you will have. A more dense foam will be stronger, have slightly better sound attenuation (STC) and can be structural, i.e. CoreCell or Divinycell, which is not meant to be insulation, while EPS and XPS are insulation products, not structural materials. Closed cell foam behaves differently than open cell foam, both in heat and sound attenuation, as well as in construction methods used. An adhesive that works on EPS may not work on XPS or vice versa. Some epoxy resins and adhesives are ridiculously expensive in the retail market. A cheap resin or adhesive could save you thousands, but if it doesn't work with your chosen materials, you are SOL.
Sit down and write a list of goals or objectives. Once that is done, you can begin to narrow down your design parameters and thus calculate an approximate cost. Until then, you are asking how long is a piece of string.
I can design (on paper) a "cheap" panel made with painted Masonite and EPS and I can design a panel with a vacuum insulated core, radiant barrier coatings and carbon/Kevlar skins. The price difference is orders of magnitude.