I agree that going the welded route is an animal in it self.
Not that its out of the question or not doable.
I could be wrong here but I believe that the stainless can be welded with filler material for mild steel but it will rust in time. Kinda defeats the purpose.
But stainless filler isn't to much more expensive.
A stick welder/arc welder uses a power source, a ground cable, a work cable and electrode holder. Which holds the welding rods of various sizes and materials. Clamp the rod in the holder and strike your arc on the joint and your welding.
A mig/wire welder uses a power source, a roll of wire in or near the power source, a ground cable and a cord with a gun at the end. The wire feeds from the main unit thru the cord/cable to the gun where its feeds into the puddle of the weld. Depending on the wire type you may use an argon/co2 mix or not. Note!! with mig when you change types of wire you also change gas type.
A tig welder again has the power source, ground cable, a tungsten torch and cable which also has a gas line to the torch. This type of welding is rather slow but very exact, also unless welding thick aluminum you can use straight argon. Here you must strike the arc with the torch in one hand and feed filler rod with the other hand, also with most tig welders you will have a foot or finger control to vary amperage. Very similar to oxy/acetylene welding. This is the best of the best for thin stuff and also for the stainless but its probably not the best choice starting out.
I would have to say that option number one is the best overall choice.
Harborfreight has a little inverter arc welder for nearly pennys, its not big and its not name brand but it will more then do what you are wanting to do along with a little extra. After the machine purchase, all you have to buy is welding rod of choice. No tanks, regulators, of gasses.
http://www.harborfreight.com/80-amp-inverter-arc-welder-91110.html
I weld for a heavy duty hobby so if I have missed something guys, pls correct me.
Here is a couple pics of some stainless counter-top I made into a shelf for my UDS.
It wasnt much welding, just two tabs to mount the shelf with and also a 1/4" round bar edge to keep stuff from falling off the tray. Stick welded, with 3/32 stainless rod.
With the Internet, its no problem at all to read and learn to hobby weld for non-critical welds.
I would still vote for bending and rivets tho, much lower learning curve, and with the experience you have, a much better chance to build a professional looking rig.