Basics

How much Electrical Current a wire, and to an extent a circuit, can carry
Important to calculate so that you don't have Electrical Fires due to Overheating
Copper resistivity - 100 compared to aluminum 160. [1]
Aluminum has about 60% the conductivity of copper, but 30% the weight for a given diameter. All together, aluminum cable is half the weight of copper for the same ampacity. [2]
- It is however cheaper, at least in terms of the conductors, Aluminum Wire Compatible Outlets etc may complicate the budgeting, but Aluminum or Copper Clad Aluminum (CCA) are worth considering

Tables - Copper

"Directly from 4-004(1)(a), you must maintain a cable spacing not less then 100% of the larger cable diameter" - [6]

At 24V we need 5A for the main power supply, so 22 ga should be good. 80C rating of [7]. Engineering Toolbox says 1 strand is good for 5A.

What are the limits to motor startup current, and common house wire? See discussion at Wire Ampacity: