Should be fine for SS with proper filler rod & flux choices. TIG, for someone relatively new to welding, has a fairly steep learning curve. So unless you have ideas about making welding some kind of side gig on difficult-to-weld metals, I'd use what I have at hand for the project described were I the one wearing your gloves.

(I'm curious why you've opted for 3/16" SS over 1/8"? For a frame that'll be covered with some other material for weather protection, 1/8" ought to be adequate as well as making for a lighter assembly when it comes time to mount it.)