Pex either red or blue and sharkbites are your friend.
The sharkbite 3/4 coupling from copper to pex and then maybe some bend supports or elbows depending on room.
Sediment filter then Neutralizer then softener then RO would be the line up.. each system's bypass will have markings showing flow.
The RO would be after 2 larger systems. a 3/4x1/2x3/4 TEE and then a 1/2 by -- for the RO feed line.
Because you have the RO going in , I would run the softener on a little higher salt setting for say 1000 gallons.
So if you where going to have the softener set at say 6 lbs and 1000 gallons, with the ro I would have 9lbs and 800gallons.. the ro will work better.
One way of doing the drain is 1/2 poly whit tubing,, if you tie the two together there should be a check valve for each of them in the drain lines.. or just run 2 lines one for each system. Do not go over 8' above the discharge point for either system.