I recommend using a joint detail consisting of a double V-groove weld. Weld from the first side, back gouge by grinding, and back weld the second side.
If you elect to use backing, it should consist of the same stainless alloy being joined to the carbon steel. If you do use carbon steel backing, against my suggestion, make sure the root bead is convex. Concave root beads have a strong tendency to crack.
Best regards - Al