David
A stick welder would be the least valuable, especially for smaller projects.
I have to take exception with your comment based on my welding experience. A good AC/DC stick welder is a very valuable piece of equipment and there are 1/16 inch stick welding rods that can be used on some pretty small projects. Additionally for about $110.00 you can get a TIG(Tungsten Inert Gas) set up(torch and argon regulator) that can be powered by the DC side of the stick machine. A small argon bottle is the only other thing you need and it is inert so very safe. With a 1/16 inch Tungsten and 1/16 inch ER 70 rod you will get a weld that is far superior to an Oxy/Acetylene weld on very thin carbon steel. Additionally you can weld stainless steel with stick welder and TIG set up powered by the DC welder. TIG welding is pretty much the same as Oxy/Acetylene as far as technique.
I did learn Oxy/Acetylene welding about 55 years ago when I first started welding and it does have its place but it is old technology. When you are building an airplane or making a repair to a component, it is my opinion that TIG also known as GTAW is a better way to go. Yes, I know that there are untold numbers of planes out there that were built with the old technology. Teaching young people in the newer technology may have the benefit of providing a career path forward as it is known that there is a shortage of young people entering the "Trades"
Former ASME Certified Welder
Former AWS Certified Welder
Former AWS Certified Weld Inspector
Current Stick,TIG, & Oxy/Acetylene Welder at Home