Indeed.  The idea of stabilizing all prices is ridiculous, because that would mean that nothing ever changes in an economy: no change in resources, no innovation, no change in people's desires.  The static schoolbook economy 101.  Prices are signals to adapt production, to correct misallocation of resources, to adapt to depletion of resources.

If prices are stable, that means that nothing can or has to change in an economy, that no resources get exhausted, and no inventions are done.

Now, if the idea is to have a "yardstick" of price (not of value !!  Price is the expression of the tension of offer and demand, and value is a measure of personal satisfaction), you can have a random basket of products, define an index on that basket, and express all prices as a function of that index.  You don't even need a currency which is a genuine asset. 

You can, as kjj says, make simple baskets with just one product, for instance: with an egg in it.  Or with a Big Mac in it.  And then you express all prices in eggs, or in Big Macs.

Eggs or Big Macs don't need to be currency.  Anything with a price can serve as a yardstick.

As prices change (by definition of a dynamic economy), prices will fluctuate as expressed in this yardstick too.  That's normal.

You can introduce a currency and try to stick it to any basket by monetary manipulation.  Or you can just introduce a sound currency, that will be its own yardstick.  Or you can just count abstractly in a debt-based system expressing debt in the index value "you owe me the equivalent of 50 000 Big Macs" without ever introducing a genuine currency.