A simple source for some good sheet steel for your project would be a section of stove pipe. They generally are in 2 foot lengths, and in diameters from 3 inch up to 8 and 10 inch. They do have a special formed edge on the long edges - that click and lock together to form the final pipe. But that would be easy to cut off. And there are generally two different thicknesses - for light and heavy stove pipe. And some is also stainless - especially the insulated double and triple wall ones. Buying new where I live they run between $5 and $6 (usd) per section for the regular stove pipe, but jump up to $20 to $30 (usd) for the double/triple wall insulated stuff. But you also get 2 or 3 whole sheets of stainless for that - when you cut it apart.
Also check out some plumbing supply places. They work with a bunch when remodeling kitchens. Stainless Steel appliances, sinks, and counter tops are IN FASHION right now, but also required for restaurants. Scraps can be available from custom fitting jobs, or from old stuff being torn out and replaced. A beat up old kitchen prep counter would have a lot of material for projects, but might be a bit thick. But a side panel from an junker stove or fridge might be thin enough.
And don't forget the scrap/recycling companies. They tend to sort stainless steel into its own pile.
Hope this helps.
Mikey - yee ol' grumpy blacksmith out in the Hinterlands