Not sure why this is in an vintage thread on cast iron if the topic is pans other than cast iron.
For pots where I am cooking liquids or other things in liquid (sauces, soups, rice, noodle dishes, quinoa, etc.) a thin pot works just fine if you stir it enough. But for thicker sauces like a thick pasta sauce I will use the fry pan. A thick chili however can be a bit too thick for such pans, watering it down a bit may be needed. First picture is a reasonably thin camping stainless steel pan, second is a very thin titanium pan.
I have been disappointed with camping type fry pans, they are too thin to cook well. But I did not want to bring a thick heavy non-stick Aluminum pan from home like I use for omelets either. Then I ran across a $10 non-stick fry pan in a farm supply store that was maybe half the thickness of the good pans, but much much thicker than the thin camping pans, and the handle was held on with a bolt instead of rivets. Removed the bolt and handle, use a camping type pot gripper and it works great as a camping fry pan. Light weight, not as good heat control as the good ones for home use but much better than the camping ones. First picture is the stuff that went into the spaghetti sauce (mushrooms, onions, peppers), the second picture the sauce later. Third picture, home fries topped with onions and peppers.
In other words, I do not need the fancy pans recommended by Americas Test Kitchen. I find a $10 fry pan to work good enough.
I think you will find a better stove to give you better heat and simmer control might be a better financial investment than a great pan on a stove that has minimal heat control.