The list was easy till you got to "refrigerator". A refrigerator in general bumps up the system size from small, 12V, to a medium 24V. I don't think a Bluetti is going to handle that, irregardless of what the ads may say. Forget about the hot plate completely. It is NOT going to work on either a small or a medium sized system. Get yourself a little Coleman propane powered camping stove for that. I used one plumbed to a 5 gallon barbeque tank for years before finally upgrading to a standard gas stove.
First, you need to understand the concept of the sunhour (sh) which is NOT the amount of daylight you have. It's a conversion factor for changing watts of panels into kWh of
solar power. Lets say you get 2 sh in winter (clear sunny day) and 5 sh in summer. We'll use those numbers in the math to come.
My cabin consumption is likely to be similar to what you need. I have a frig on 24/7, lights, TV, and a laptop. I might consume ~3.0 to 4.0kWh of power per day, with everything on. Remember that the inverter being on consumes power to. A good rule of thumb is that the background consumption of the inverter is proportional to it's size, but also proportional to the quality of design. I have a quality Schneider XW+6848 inverter that uses 30Wh, or about 0.72 kWh per day. Cheaper imported inverters, typically the AllinOne types, have far higher consumptions in the range of about 1.4-2.4kWh per day.
So, let's settle on needing needing 3.0kWh of power per day, or 3000Wh. You divide the power needed by the sunhours. So, in the winter, you'd need.... 3000Wh/2.0sh = 1500W of solar panels. In the summer though, you'd need just 3000Wh/5sh = 600W of panels. Plan for the worst day, not the best, and the system will never let you down. Plan on installing 1500W of panels. Grid-tie panels are dirt-cheap right now. I just got 260W REC panels for 65$ each this year. That's only 390$ if you buy six of them. Don't buy little 12V automotive panels. You pay a hefty price premium for panels designed for automotive. Don't buy panels
online. Search for panels on Craigslist and go with cash and carry pricing. Expect to get 2-4W/$ with
local pickup.
You might get by with fewer panels if you put them on a single-post rotating array frame like I did. This frame holds 4 grid-tie panels in portrait, though can hold 6 in landscape. I made 5.1 kWh in February with just 1000W by rotating from East to West over the course of the day. My frame adjusts for both azimuth and declination, so I can really maximize my solarization.
You need a charge controller to connect the panels to the battery. Assume though that you don't get more than 85% of power from your panels with day to day usage. With 1500W of panels the math is 1500W/25Vcharging = 60A. De-rated to 85%, that's 51A. A 50A controller like Epever's Tracer 5415AN would be OK. You could wire two parallel strings of three panels each into it. You would write that in shorthand as 3S2P. With just 1000W of panels, you could go with a smaller (cheaper) Tracer 4210AN controller, but there's less flexibility with the smaller controller. That has to be wired 2S2P
In a cold climate, Li batteries do not work well. Lead-acid is less likely to get cold-weather damage if they are kept charged. CostCo makes a 6V 210Ah golf-cart battery that is still on sale right now for 99$ in the US. Assuming you don't want to drain a lead battery lower than 50%, then what you get is.... 210Ah X 24V X 50% = 2520Wh, or ~2.5kWh. That's not much, but it will get you through the night. You have to decide how much cloudy/rainy weather you need to get through. Multiply your {(days needed X 3kwh)/24V}/50% to get the size of your battery. Let's say you need 3 days... The math is {(3 days X 3000Wh)/24V}/50% = 750Ah. Those would be a lot bigger batteries than golf-carts. Expensive, but doable. Might be cheaper to go with a smaller 400Ah battery like a Trojan L-16, and get a generator to top off after the rains start.
Now the inverter. Do NOT get a cheap square wave or modified wave inverter if you run anything with an electric motor. That includes refrigerators, freezers, pumps, compressors, and power tools. Get a good quality sine-wave inverter. There are two types, high-frequency transformerless inverters, and low-frequency transformer based models. HF is cheap to make but they don't have any starting surge. LF is more expensive, but can start your power tools under load. Take a circular saw and press the blade into a 2X4. Then press the start button. You'll see the difference.
I've seen complaints that the smaller 1000W inverters would not run a refrigerator. A 2000W 24V sine-wave inverter is a better choice. Samlex makes a nice sine-wave 2000W inverter, though it HF. Schneider makes the LF 4024, which I have in my
workshop. It can run a 1.6hp air-compressor, but it costs 3X the price of the Samlex. But, I'd never expect the Samlex to run a compressor.
So, what is this going to cost....
six panels 400$
50A charge controller 250$
four 6V batteries 400$
HF inverter 650$
1700$
Buy some steel to make a nice array frame, sink it in
concrete, and wire it all up. Add another 300$ for steel concrete mix, and good copper wire. Call it 2000$ total. Price goes up though as the size and quality goes up. Factor that in proportionally.