You don't need to insulate, but it is always at least mildly a good thing if you happen to feel like doing it.
The cheapest insulation is... drumroll please... whatever you can scrounge
If you have to pay cash money at the hardware store, I think fiberglas batts are going to be cheapest. Some people are trying lots and lots of plastic grocery bags filled with styrofoam packing peanuts, fwiw. Sawdust is a traditional insulation but you'd need to be really REALLY REALLY confident that no moisture will ever get into your walls, like thru leaks at the edges of your siding or windows, or drifting in thru minute gaps under the eaves, b/c if sawdust gets damp it will rot out your main coop structure and that's no good at all
Most of the above have some capacity to become a mouse farm; rigid foamboard is least susceptible to that.
Pretty much all of the above will need to be covered by something peckproof on the inside, so chickens don't eat the stuff and get sick.
Good luck whichever you decide, and have fun,
Pat