I would use something like a 3/8" 2 flute ball endmill for a medium sized fuller. Don't try to do it all in one pass, and lock your Y axis.
If I wanted something fancy I'd look for a helical gash, some kind of coating, and a geometry specifically for stainless. MSC's Accupro brand goes on sale a few times a month and some are available with geometry specifically for machining stainless. Actually, their aluminum milling cutters work well finishing stainless too.
OSG has some really good stuff for finishing milling in tough materials, but it is spendy.
If you're not planning on finishing it manually (sanding or stoning) after milling, this is one of the few times where I would actually use oil or neat coolant.