I compare such a situation at home akin to what I need up at elk camp in my wall tent. I would refrain from using a propane heater unless it has the catalyzing feature that prevents the production of carbon monoxide. These heaters also have an O2 sensor that will shut down the combustion system if the O2 gets below an acceptable level. I've used these in smaller spaces (<500 sq ft) with decent results in fairly cold environments and always been satisfied with their performance, knowing ahead of time their limits. I've always used the smaller versions, though I understand they now have a bigger model with twice the burning surface. I also hear that there are more permanent fixtures that do the same thing. I've been in cabins that use the non-catalyzing heaters, and sleeping in the top bunk under those conditions is not an option for me. I've also been in wall tents with bigger non-catalyzing Mr. Heaters going intermittently through the night to augment wood stove heat at times. It is acceptable because the tent was breezy enough that it purged the exhaust gases sufficiently. At home, I would tend to keep at least one window open per 1,000 sq feet.
As far as propane stoves, I have come to the conclusion that nothing out there is as good as the Camp Chef line of professional outfitter grade cast iron stoves. At 30,000 btu per burner, I find that the two and three burner units can handle all my camp cooking needs, including heating gallons of water in minutes, cooking in my largest cast iron dutch ovens and frying pans, and grilling steaks and such at the ideal temperatures. While not of the backpacking variety, they do well in the back of my pickup or suburban, are quite rugged and durable, and use the 20 lb propane tanks or similar. I used to use coleman stoves but found that although they were much more portable, they lacked the size and heating characteristics that I desired for how I work. They will do the job in a pinch, but when portability isn't such an issue they are just not nearly as convenient or reliable.
There are other cast iron stoves out there, but my experience has been that the Camp Chef products are superior to anything else I've seen. I don't owe them nothing and don't expect nothing from them, so this here plug is legitimate. Costco's sold the 3 burner Camp Chef stoves previously for as low as $150, but I haven't seen them in their stores for a while now. Online they are almost double that, but still well worth the $$. There were more than a few nights when living in my cook's tent that I left one of the burners running on low all night long to supplement my poor little woodstove, without any problem and more than enough comfort.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)