You need to add up all of the watts of the things you are running. Then multiply by the hours you will be using them. That gives you the watts/hr.
Trying to keep batteries charged to power that stuff is going to go through a ton of cycles. That wears out traditional batteries.
You will need deep cycle batteries or those used on solar applications.
Your issue is going to be in trying to keep those batteries charged. Depending on your location, it might actually be a decent case for a small solar set up.
Wouldn’t a generator a few hours a day keep them charged?
1) IMHO post #10 is wise. Start there.
2) Before going into the calculations below, I'll add here that you can always make sure your equipment is stackable to upgrade later if you need to. For example, if buying one small battery and trying it for a while doesn't work, fine. You can add a second battery later on a bus. Same with adding a solar panel later. With my experience, my math in the planning state you're in but for my home was fairly accurate, but I started with a much smaller system for a year than I knew I'd want in the end just so I could see how it handled all seasons. After that I upgraded it to the system I have now. In your case, perhaps the only thing that would be important to make sure you get right the first time is inverter/charge controller capacity. (I later added a 2nd inverter, but I have more room in my garage than you have on a houseboat.)
2a) I'm a data-centric person. I'm happy with my Sol-ark inverter (later upgraded to 2 inverters) in large part because they record telemetry every 5 minutes that I can export into Excel spreadsheets and import in a SQL database and crunch numbers. A year's worth of data for all 4 seasons in different weather helped me see exactly how much of each solar component I should upgrade to take advantage of the economies of scale (invest more to get higher ROI), but not so much I'm fighting the law of diminishing returns (invest more gets lower ROI). Basically, I win the battle on the averages without trying to be completely off grid. Much like you'd probably be willing to use your generator every now and then, but would like to minimize when feasible. If you're not quite that heavy on raw data, I suggest at least get an inverter that provides a few graph outputs so you can see it summed per day, per month, etc.
3) Another tip is to be hip to how much the peak solar hours change per month in your area. Use this tool, enter your city, then click Results. For me it says in January I get 3.4 hours, February I get 3.9 hours, etc. (numbers below assumes yours is the same) Let's say you calculate from post # 10 that on an average day in January you consume 5 kWh and want to know how much solar you'd need to handle an average day in January. 5 kWh / 3.4 peak solar hours = about 1.5kW (1500W) of solar panels. Assume a 10% reduction converting DC to AC. (You'd need 10% more panel wattage just to break even on an average day, so call it 1,650W.) Repeat that for all 12 months. Of course, include a little extra for margin. (Unless you're trying a small system for a year like I suggest in step 1.)
4) Battery storage: Assume another 10% loss when storing power to the battery, it sitting for a while until night, then later retrieving the power from battery. In all of 2024, the amount of power I discharged from the battery stack was 9% less than the total stored to the battery stack. Of course not all of the solar power coming in would go straight to battery because some would be immediately converted to AC to power the load. So you don't need your entire battery stack for the 24 hours of power consumption. But you do need extra solar wattage intake knowing that the night time power consumption will first go through a 10% loss for storage, before going through another 10% loss converting DC to AC like daytime power does too.
5) Depth of discharge and wear on batteries: The way I handled it for my home was to simply buy more battery storage than I usually need to power through the night. But I have more room in my garage than you do, so maybe it's not as easy for you. I've set my inverters to not let my battery stack to get below 30% charged before they start pulling from the grid (again you won't have a grid, but you might decide a similar floor before running a generator). Yet, my system usually doesn't drain below about 45% or 50% anyway. So usually (not always), I'm not taxing my batteries a lot with a huge depth of discharge. The hope is that this makes them still working well beyond their 19-year/50% usable warranties.
6) If you have something else on your houseboat that's battery powered that you don't have to charge all the time (i.e. hand tools, electric shaver and toothbrushes), you might consider an inverter that has what my Sol-Ark calls "smart load". Though this isn't exactly how you'd use it, here's how I do it. When my battery stack is at least 70% charged (or whatever I configure it to different times per year), my inverters will power an intermittent electrical panel that I use for usually charging my EV. The idea is that if my home battery stack is charged to 70% or more, my home will power through the night without pulling from the grid nor draining my battery stack too much on average. Combine that with the fact that my EV doesn't need a charge every day (230 mile range if charged to 80%, and we drive it about 50 miles per day, so we can have a few days in a row of hard rain before we give up waiting for free solar and decide to charge the EV with grid power). Thus we usually keep the EV plugged into a charger from the intermittent electrical panel (not always on, but if it is on it's always free power). But if we come home in the EV with less range than we need for the next day, we charge it with a charger tied to the constantly powered panel (always on, but not always free). The end result is our EV is almost always charged with free power. Basically, my EV's battery acts as a kind of extra storage for my home (though my home is never powered from the EV battery, just saying the math and usage make them work in concert).
Now using the example above, but for you without an EV. If you have some 120V outlets in your houseboat that are intermittently powered, next to outlets that are constantly powered, you can charge your battery powered hand tools, emergency jump box, hygiene battery tools, phones, laptops, etc. (anything with its own battery) almost always by simply keeping them plugged into the intermittent outlets. If on a string of rainy days you need to charge those hand battery devices, then plug them into the constantly powered outlets. So you have dependable power when you need it, but yet winning on the averages by utilizing intermittent free power when you can (for devices that give you flexibility because they have batteries).