How do I renovate 45 year old aluminum wiring for a new outlet for a new cooktop and range?
I would use metal boxes. Much more sturdy and not very much different in cost in the grand scheme of things. 

You mention that aluminum wire was used to the stove. Was that aluminum wire fed all the way back from the main power panel? If so then you'll likely have an electrical box with a receptacle mounted to it that connects to the AL wire. Make sure to purchase a socket assembly specifically designed for deployment with AL wire. (That is of course unless you will be replacing the feed wire back to the panel with copper).