Here's the recipe:
For wires other than the common, use wire with an ampacity that is at least that of the overcurrent protection (circuit-breaker, fuse, or electronic current limiting) of the circuit. For example, use 20-AWG for up to 5 amperes, 18-AWG for 7.5 amperes, 16-AWG for 10 amperes, 14-AWG for 15 amperes, 12-AWG for 20 amperes, 10-AWG for 30 amperes. The ampacity doubles every 4 AWG sizes.
Find the worst-case common current for each transformer. For a traditional transformer, that is the circuit-breaker rating, 5 amperes for a 1033, 10 amperes for a KW, 15 amperes for a Z or ZW. If a transformer has individually protected outputs, add their current ratings. If a transformer has both an overall protection and individual protections, use the smaller of the overall rating and the sum of the individual ratings.
Add together the worst-case common currents for each group of transformers that are all in phase with each other. (That's just one group if all of your transformers are in phase.) Select the greater of those two currents as the worst-case common current.
For any wire closer to the layout than the point where the individual transformers' commons are connected together, use wire with the ampacity just calculated. For example, 2 type-Z transformers would need a 10-AWG common after the point where they are wired together.
There is no electrical difference between solid and stranded wire of the same gauge. Stranded is simply easier to work with.