IMO, if the pony is rising 4 there is no harm in starting him over crossrails; but I wouldn't jump much higher than 18" this year. However, there's lots of useful training you can do with poles on the ground and crossrails.
I like your pony a lot, he seems like a good, useful sort with a lovely attitude.
His head carriage is quite nice, I see no reason for a martingale. The bucking may be normal green pony naughtiness, but the rearing needs to be addressed promptly. If he rears while you're getting on, he may not have sufficient balance to support your weight at a standstill OR somone might have agressively restrained him for mounting while he was being broken.
Investigate your saddle fit, and whether or not his back is sore and involve your trainer to get this figured out.