Welcome to the Forums and congrats on your "project".. (We call all our Airstreams projects in some form or other..)
As new members, you are obligated to learn to use "Search" tab in blue bar above, which is now available as a registered member... Just type in works like hardwood or pergo or laminate floor and you'll be amazed at the number of threads that pop up, with photo;'s of others' replacement flooring projects..
Lots of owners have gone with pergo or other laminates, or combination of wood with carpet in rear bedroom areas. Several brands work well, so long as allowed to float to accommodate trailer flexing in motion... Others have successfully put down cork floors (see Uwe's thread on a 63 rebuld..) or wood-looking linoleum sheet.
As for appliances, hot water heaters come from Atwood with electric rod options to avoid need for gas, though they take good 110V circuit. You can always buy electric heater (ceramic or oil-filled radiator type) to heat interior, though those choices won't heat water and waste tanks under floor surface as installed gas furnace will. Small electric refrigerators might not be perfect fit, but they can be installed to replace existing unit. You're left with trailer that can't be "boondocked", but that may be acceptable tradeoff.. Value to any future buyer will be reduced...
In Theory, there's no difference between Theory and Practice, but in Practice, there is usually a difference...