Peter,
Welding stainless with TIG isn't too tough. Your biggest challenge will be dealing with distortion, as stainless steels don't conduct heat away from the weld joint as fast as mild steel. The other issue with welding stainless is preventing the back sides of the joint from oxidizing or 'sugaring'. There are two ways to avoid this. If welding on an enclosed object, the inside or back side of the joint can be purged with argon shielding gas. If welding a T joint, or some other joint where the back is exposed and purging isn't practical, then you'll have to train yourself to weld fast and minimize heat input on the weld face. This will limit the temperature rise on the weld root, and surrounding metal, hopefully to the point where sugaring won't take place.
The major concern with sugaring, is that the heat has caused the stainless to lose some or all of it's corrosion resistance in the weld heat-affected zone.
Your weld faces should be bright, or have a kind of rainbow hue of blue and yellow tint. Anything Dark grey or black is a sign that your shielding gas coverage isn't adequate.
If this happens, focus on maintaining the proper work and travel angles for your joint, and minimizing the arc length. You might also look at using a gas lens, instead of a standard cup on your TIG torch. These cost about $15 at my LWS, and they dramaticly improve shielding gas coverage. The downside is that gas lenses can limit your view of the weld joint, and do not fit well in tight spaces, like inside corners.
Last thought, stainless steels are not often harder than mild steels. They are harder to machine because the material tends to toughen as it's worked. Stainless also tends to smear and therefore is harder to machine.
Good luck, and if you need more advice, ask away...
