As someone with a degree in economics, I've basically come to the concluding that it's impossible to do in a non-arbitrary manner, or at least extraordinarily impracticable.

To show why, think of your question about prices. The obvious question is, how are prices determined? Well, (assuming for simplicity that government policies aren't affecting it) you need to look at supply and demand.

Start with demand, which when we're looking at an entire economy is really aggregate demand, so essentially an equation made by combining a bunch of other equations. A simple way to model aggregate demand could be:

QDx = C - Apx - Bpw + Epv + FY

Where QDx is the demand for good x, C is a constant, Apx is a constant A multiplied by the price of good x, Bpw is a constant B multiplied by the price of good w, which is a complement to good x, Epv is a constant E multiplied by the price of good v,which is a substitute for good x, and FY is a constant multiplied by the level of income in the economy.

Now if you had these equations for every good in the economy, things would already be incredibly complicated. But where do the values for that equation come from? To figure that out, you'd need utility functions and budget constraints for your consumers, which would be even more complicated. Even ignoring the complexity, they would also be arbitrary. You have no real consumers to talk to about this, so you'd just be inventing preferences and then using those to derive prices. In that case, better to just start with the prices and save the math.

The only realistic option is to just go with what feels right. Figure out what common good in your world you can use as a baseline, then think of other products as units of that. Just keep in mind the basic laws of supply and demand and wing it