Adding a drain for water softener

[johnshapes]

Hello all, looking to add a drain for a water softener that I am getting very soon. The water softener will be installed to the left of where the main water supply comes in. To the right of the main supply line there is a 3 inch drain stack pipe that is connected to a toilet, shower and sink on the main level. I'm thinking I can just put a T in the drain pipe and install a short piece of pipe with a trap and then a riser piece and some sort of one way valve.

Im unsure if this would be legal and im wondering what size pipe I can use, length of riser (if needed) and what kind of valve/trap I need. Thanks for the help in advance.