HI,
I would recommend a small inverter. Something in the 150 - 300 watt range will be really energy efficient. I rarely use my 1500 watt inverter, and when I used it for cooking in the microwave, the microwave never cooked as quickly again, so I had to replace it.
WHen watching TV with my 1500 watt inverter, the draw from the battery might be 6-8 amps, while plugging in the 150 watt inverter and shut off the big one, the amps will drop about 2 amps.
I have 4 golf cart batteries, 67 pounds each, or around 300 pounds including the larger wires. WIth a camper, I would only recommend a pair of batteries. I had one under the hood of my gas F-350 and did not have one inside the camper. This helps bring more weight over the front axle, but there is not room with a diesel engine (that has dual batteries to start the engine). You might have space for a max of 2 batteries? That limits you to storing about 1,500 watts, and if you want the battery to last more than 3 years, do not discharge them below about 50%, so about 750 watts before recharging.
I have a 400 watt solar system, and it can make up 120 amp hours daily. I would recommend at least a 140 watt panel, you will not need nearly as much battery capacity if the solar is making up for the power consumed during the day. Your propane leak detector, CO meter and refrigerator will use about 1.2 amps all day and night, or around 35 AH daily. This is your 'base' load, before any other lights, pump, furnace ect, are added to that load. One 140 watt panel can make around 35 -45 AH daily, in full sun. It will also shade part of your roof, so it will be slightly cooler inside. Also I run my fantastic fans (3) so it is usually cool in my RV!
SunElec.com sells a 140 watt 12 volt nominal panel for around $229. Add a PWM controller, and some #10 UV rated grey romex from HOme Depot, you have a system. Mount it to the roof with 6" long brackets - 2" angle aluminum with 3 holes 3/16" for #10 screws into the roof, and 5/16" hole for the 1/4" bolt into the panel frame. (do not buy home style frameless panels). This will mount the panel about 1" above the roof, for cooling air under it, and will increase output when cooler.
Good luck,
Fred.