Things I would want to know are:
What kind of thermoplastic? ABS, PVC, PE, PETG, ACRYLIC, POLY-CARBONATE, STYRENE, or, one I left out?
The type of tool/die is this part being molded against. Male or Female?
The material of the tool, as in machined aluminum, cast, epoxy, wood?
How much draft are in the sides?
Flange, no flange?
A picture/drawing of the part?
You might get a dimensional sample on the 40mil, although a bit weaker than the 60mil. The thicker material may help keep it rigid enough to come off the tool with less distortion if using a male mold. Male molds can make a good part with less thinning, but the sacrifice is a larger sheet. Which does create addition problems once formed if it doesn't come off the tool easily.
A female mold can thin out a lot more in the corners, but you should be ok with that amount of plastic inside the mold. Starting out at 40mil, could thin out the corners to around 10-20mils.
Get quotes from several different formers. The quantities you plan on and the prices you have in mind for its purpose can change the tooling cost significantly. For prototypes, I'd rely on a fomer that knows the material and could show you similar parts they have formed. I am sure most respectable forming shops will guide you in the right direction. Just know when to pull the plug on them if you start getting bilked for their extended learning curve, getting it to form.