Since this is not a pre-qualified joint in AWS D1.6 "Structural Welding Code-Stainless Steel", I'd recommend qualifying a weld procedure first:
I'd also suggest applying an single pass overlay layer of E309 s/s on the carbon steel side of the joint, then weld to the 305 stainless steel side with E308 electrode.
Another approach wold be to use an ASME Section IX qualified WPS. If you have P8 to P1 this is an acceptable combination.
If had this weld to perform, absent job specifications to the contrary, we would weld the complete joint using 309 filler metal. We would use GTAW/SMAW processes.
Charles Hall