You can forge most 300 series and 400 series stainless steels, but they are all quite hot-short, so you can only hammer on them in a certain range of heat. Too cold and it shatters, too hot and it crumbles. It will take some pratice to get the ehjat just right. try not to do this in daylight. I find it extremely difficult to do small forgings in daylight. I prefer night, but a really dark soot covered smithy is OK too.
You can use 304 stainless steel, it is quite common and can be hot forged, but there are better alloys.
321 and 347 would be better, but they are also harder to find in bar form.You could go for a white bronze like 70-30 Copper Nickle. It is a dull silver color and forges quite well, with better control and lower heat than stainless steel.
Propane is actually better for forging stainles steel than coal. Coal forging tends to imprt more carbon into the steel. Thsi is very bad for stainless since it often lleads to the formation of chromium carbides.
400 series stainless steels are what knife blades are made from. 410 is the easiest to work with. It is used a lot for stainless rulers and fish knives.420, 430 and 440 are used for knives.
Most stainless steels have to be passivated after hot work or welding to remove free iron particles from the surface, or you get rust spots.
Hence why I think that 70-30 Copper Nickle is a better choice.