Some of these Replies are Outrageous and so far from Fact it is Unreal. However; you got to start somewhere, if you don't know the answer it is easy to come by when searching in the correct place.
Stainless can easy be welded to Carbon Steel. When joining Stainless to Carbon Steel it is Best to use a 309 rod, but in a pinch 308 will also work but not as well. Stainless Steel is easily welded without any Harmful Vapors and/or effects, if it was any different then I would surely be dead a very long time ago. In Fact ANY Metals can Be Welded together. New tech has come forward that will both astound and enlighten you when it comes to welding. Friction welding can weld many various dis similar metals with a seemingly Seamless weld joint. In Aerospace projects Friction Welding is used to join Aluminum to other Metals(Steels.Titaniums,etc.)
Any Galvanized Steel should NEVER-EVER be Welded or Cut or Ground on without a Respirator that is specifically for filtering out the Galvanized Material.
And Remember that Stainless Steel is NOT Totally Rust Proof or Corrosion Proof. There are 150 Alloys of Stainless Steel of which 15 are commonly used. I laugh all the time when people refer to Stainless are being truly Rust Proof. One needs to think in Terms of Corrosion and away from Rust nomenclature.
As for the OP's question Yes, you can weld Stainless to Steel. The Varying Thicknesses or Gauges do pose a Situation but nothing that can not be overcome. I suggest that in your Application you take your metals project down to a TIG welder, he can easily weld these 2 Metals together to give you a solid container Vessel.
As for the Galvanic Issue of Dis-similar Metals coming into close contact. Think in Terms of your High School Chemistry Class and the Periodic Table of Elements. The Galvanic Issue if when Dis-Similar Metals exposed to an Electrolyte (water for one) cause these Dis-Similar Metals to Corrode at a Hyper Speed. This Same Effect is what your Car Battery Does to produce Electricity. When One Metal acts as a Anode and the other metals acts asa Cathode in this Electrolytic solution. It could be water, or as in the case of Salt Water, Metallic Ions migrate to the Anodic Metal which corrodes at Hyper Rates leaving the Cathodic Metal corrosion retarded and even stopped. Have you ever witnessed the Sacrificial Anodes(Zinc) on SaltWater Boats ? These Boats in Salt Water have a Aluminum Engine but Stainless Propellers, and/or other Dis-similar metals. A Sacrificial Anode(Zinc) is then placed onto and below the salt water to sacrifice itself so the Aluminum will not corrode at this hyper rate. Hence the Corrosion in the Mixed Metals in the above post about the Piping, etc.
I have been Fabricating for Years with Metals and currently Employ both Mig and Tig welding in my business of high performance design/fabrication/welding of vehicles(bikes,cars,race,4x4,etc.) However; even though I have years of experience we all have the ability to learn and grow our education. That's the whole purpose of this and other forums. The Internet is a wealth of knowledge and if you are interested in Fabrication and/or Welding why don't you first stop by
www.weldingweb.com
and
www.weldingtipsandtricks.com
or ask questions on here, just take with a grain of salt some of the answers and as always get a second opinion if necessary. Good Luck with your project. Let us know how it turns out.