I can't speak for woodies (but I'm sure they're similar), but mandarins are seasonal layers - they may lay their first spring, but usually, the second spring is best for hatching. One or two clutches max per spring. I'd say go for the juveniles - mandarin eggs apparently don't ship well at all - and although artificial incubation CAN be successful, its a science, so its best if they're naturally incubated.
Mandarins are a wild species, as opposed to a domestic breed, and they tend to be extremely skittish even if they're hand raised. They DO fly, and fly well, providing they're not clipped or pinioned. They require a large planted enclosure that is covered and escape/predator proof, and access to water for swimming/bathing - otherwise, if you plan to turn them loose in the yard or on an open pond, they probably won't stick around long.