Well hello there crazy stove person!
The way to go is to get an old stove. There are several REALLY GOOD brands of stoves from the 40s/50s that are hands down better than modern stoves. Even better: These are stoves that were cadillac brands that sold for over $3k in todays dollars. They can be found for a few hundred bucks on craigs list.
When we built our house, DW had already pre-decided on make/model. Our kitchen was designed around a 50s era Chambers 90C. I'm not sure about the other popular brands, but Chambers definitely has several online forums and several facebook groups dedicated to restoration and repair. These forums are invaluable. Everyone on them has been there before and has rebuilt/restored stoves.
If you take time and wait/watch craigslist, you can generally find a 50s era Chambers for $100-300. Stoves you find will generally be working ... and minimally will need cleanup, possibly restoration. I've bought 3 Chambers for an average price of $100. Our daily use stove, fully restored, probably ran us about $800 with me doing all the labor. This includes fully rechroming everything and includes me selling off surplus parts to try to recoup some costs. Our "full restoration" did not include re-porcelain... It looks very nice, but it does not look like it just came off the showroom. Our goal was to cook on it, not make a museum piece.
Here are photos from restoration. I started with 2 stoves (1950 and 1951) and combined them to make one working stove.
https://goo.gl/photos/UkyUvTD9b7Sh4uov8I still have one cooktop from late 1950s/early 1960s that I have not restored but plan to "some day." I plan on building a rolling cart for it and using it for outdoor cooking.
Are these appliances safe?
Absolutely. Most people do add a safety valve/standing pilot for the oven. Safety in appliances is based on keeping them well maintained. My mom had a modern stove with electronic ignition. She had alzheimers. She turned on the stove top and walked away and the electronic ignition failed. I just happened to visit her and the kitchen was full of gas. Moral of the story: New isn't necessarily safer.
The problem with gas is that condensation from the combustion process can cause rust out, so check that Dixie out thoroughly. Standing pilots will accelerate the problem (and waste gas). And baking in a gas oven (new or old) tends to be uneven, hence the trend for new ranges to have gas burners and electric oven elements.
The main problems I've seen with rust is not from combustion but from improper storage. You will sometimes get light rust on oven burners, but these things are heavy cast iron things. Brush it off and it's fine.
Standing pilots really don't use much gas. Certainly they use less than none... but it's very small.
And let me assure you: not all gas ovens cook unevenly. We had never had a gas oven before this one. Now I could never convince my wife to go back. Our "second oven" is a modern electric wall oven. My wife is constantly scheming on how to rip that out and replace it with a 1950s gas oven. Other than overflow cooking for Christmas/Thanksgiving, the modern oven is used as a storage device for cookware.
A Chambers oven is SUPER insulated. It also contains quite a lot of heavy cast iron parts. This leads to very even heat. It is also designed to cook "with the gas turned off." You generally cook a while with high heat, then turn the stove completely off and let it coast for several hours. When the oven turns off, the air intake and exhaust clamp down hard and hold the heat inside.
