Yes, pure SIN wave inverter. No reason to not get this, and some items will be ruined from a modified sin wave inv.
1500/3000 at minimum.
Keep in mind that smaller inverters draw less phantom power than big ones, so getting a huge one and having a lot of extra capacity is not ideal. Size it for what you need, or get a 300 watt inv and a 4,000 watt inv and use the one u need. For me a 300 pure s w i is all I need or running laptop charger or other small things.
You are in a camper. Yes, electric appliances and devices are clean and easy to use. Campers run off of propane. Do as much propane as you can. Propane furnace heater (the blower motor will still draw a lot of watts, but not as much as an all-electric heater), or a Buddy heater (which puts a lot of moisture into the room), stove-top coffee maker (see espresso pot) or pour hot water over a filter attachment.
an electric TV is fine as it will not draw a huge amt of power, as long as you dont binge watch tv.
Keep in mind, with solar you want to do electric things (charging phones/devices, tv etc) during the early sunny part of the day so you can use the sun and not the battery, and so your battery has time to recharge before sunset.
A small electric coffee maker in the morning prob not a big power draw, but only if there is enough charge left in the batteries after running TV at night, furnace fan at night, charging phones at night... because you have all day to re-charge the batteries
Get the picture? Night is not solar's friend.
An electric stover-top (those new induction ones) might be fine if you use it not-very-often as you say, and if rarely used does make more sense if you have the power to run it.
Marine batts can be run down about 200 times, real deep cycle about 1,500-2,000 times, a car starting battery about 2 times. Even so, every time you have an electric draw you are running down your batteries, so running it down 1% 100 times is similar to running it 100% once. (thats not the exact math but gives u an idea that you dont have to run it down to shorten the life of a batt, you just need to run is down any amount, and those amts add up).
Get a good charge controller. MPPT or PWM. I prefer MPPT.
You dont need a $500 one, you should be able to ebay it for $50-$80.
Solar is great. Get real glass panels, never the "flexible ones" as they are only good for when you absolutly have to have a bended one.
Run the solar in as higher voltage and let the controller drop the voltage. Higher voltage 36 volts or more is more efficient over the copper wire than lower 18 volts. You can use less wire, and smaller wire this way. controller goes as close to battery as possible.