I swear, there's just no way to write this briefly, honest! I'm not a blabbermouth! Really, I'm not! Ask my mom!
I have no financial interest in any of this stuff, it's just the result of my own research for my own camper.
The reason I like to start with what you want your daily routine to be rather than just guessing at battery size or relying on what worked for someone else, is that it ensures the system fits your lifestyle, rather than altering your lifestyle to fit the limits of the battery you bought and are stuck with, or spending a lot more for something huge, complicated and overweight that you don't need in order to be safe. It's a pain to start making lose-lose decisions like "well, I can either run my lights until midnight reading every night or use the electric coffee maker every morning, but not both." Especially in the middle of a trip. I'd rather be able to do both if that's what I want. Or even fall asleep with the light on all night and not worry about being in a blackout for the rest of the trip. If there already was a battery in the camper when you bought it, you'd probably have to modify your daily routine to work within the limits of your system, unless you prefer minimal-tech camping, using oil lamps, water jugs instead of a pump, etc.
If it helps to use an analogy, you can think of your battery as a home gas tank that you can only refill every three days (as you said, the length of your longest trips), and the appliances are different vehicles that all get different mileage. A space heater is a Hummer, a light bulb is a Civic, an LED light is a moped. If you want to make sure the tank lasts the whole three days without buying a larger, more expensive tank and lugging the weight of more gas than you need, you need your most accurate estimate of how many miles each "vehicle" will be driven during those three days, and the mileage each one gets. The wattage or amperage consumption on the appliances is the "mileage" for each "vehicle". Just gotta add 'em up and compare the total to the size of the tank. If the tank isn't big enough, you either have to drive some of them less (compromise your lifestyle), refill the tank more often (recharge the battery), or get a bigger fuel tank (bigger battery).
Another analogy might be a water tank used to water your various pets, again only able to be refilled every three days (unless you have a generator), with pets varying from crickets (LED light) to cats (12v light bulbs) to elephants (A/C), and you knowing how much each one drinks every day, and compromising on which pet goes thirsty if your tank is too small.
Having a generator lets you refill the tank whenever you want, when you're boondocking without neighbors or in a campground with generator hours allowed (or to a possibly lesser extent solar panels). But not everyone can afford one, especially a quiet one like a Yamaha. And not everyone is willing to put up with the noise etc. of having one (and solar is expensive and can be complicated to install if you're not familiar with it, and requires more math to make sure they put out enough to keep up with your usage, including cloudy days). You can also put a battery isolator switch in your tow vehicle, rig up a cable to the camper, and use your car's alternator to charge the battery, which is great while driving and a very useful addition for rolling trips because it ensures your battery is topped up when you arrive at every campground, but is pretty expensive fuel-wise when parked.
"Marine" batteries are not real deep cycle batteries, they are slightly more rugged versions of car batteries. Both are designed for starting engines, which requires a massive surge of amps for a very short period of time, so they have lots of thin lead plates with large surface areas in order to "give it all they've got" until the engine starts. In the Olympics they'd be sprinters. Discharging them deeply erodes the thin plates and shortens their lifespan dramatically, so they're not very good for camper use, which tends to extract every last electron out of a battery before it gets recharged. Real deep cycle batteries have heavy plates that don't erode much as long as you don't discharge them below 20% (50% is better for longest life), and are designed specifically for long, slow, deep discharges. They'd be the Olympic marathon runners. They cost more but last years longer. Worth the money in the long run to get a REAL deep cycle battery, IMHO. Most car batteries and marine batteries don't even tell you how many amp-hours they supply, because they're not intended for that kind of use. They're always sold by cold cranking amps, which is next to useless for our purpose. I wouldn't use one unless it was all I could afford, and I'd make sure to have a way to recharge them, even on an overnighter. My van battery, after running my furnace, one or two lights, and a radio (whose draw didn't even register on my ammeter) overnight needed to be charged with the generator before it would start the van, and probably took 10% off it's lifespan using it for that.
In a quick Google search I found this good small Trojan, 85 amp-hour, real deep cycle Group 24 (24 is a common size used in campers, it's car-battery sized and not that heavy, 47 lbs, and Trojan makes good batteries) for $134.95, plus freight charges (because "wet" lead/acid batteries can't go by FedEx or UPS, freight shipping can be expensive because of the weight, but no doubt there's some place like Battery World near where you live that would have something similar):
www.batteriesinaflash.com/deep-cycle-lead-acid/12v/trojan-24tmx-12v-85ah-group-24-flooded-deep-cycle-batteryThe 80%, maximum-available-without-damaging-the-battery capacity of the above 85 amp-hour battery would be 68 usable amp hours without recharging. That would run one 2-amp light bulb for 34 hours (2A x 34hrs = 68 AH), divided by three days would be 11.3 hours per day. It would run a 4 amp propane furnace like mine for only 17 hours, or 5.7 hours per day. If you ran both at the same time, it would run them for 11.3 hours, or only 3.8 hours per day over three days. 68ah / (2A + 4A) = 11.3 hr, / 3days = 3.8hr/day. That battery would be tough to live on for three days without some way to recharge during the trip, and it's a very common size used in campers.
The same battery would, fully charged, run a 1000-watt, 110v AC space heater, through an inverter, for 45 minutes.
1000W / 110VAC= 9.1AmpsAC to run the heater on full.
9.1Amps AC x 10 (conservative estimate of inversion cost in DC amps to make one AC amp through an inverter) = 90.9 Amps DC to run the heater on full.
68Amp-hours / 90.9A = .748 hrs, x 60min/hr = 44.88 minutes, or about 15 minutes per day, which ain't much heater time.
There's a true deep cycle, sealed AGM, 75 ah (usable 60ah at 80% max discharge) battery here for $175.95. AGM means Absorbent Glass Mat, which is a safer type of battery in that they can be put in any position because they don't leak, they don't vent gas when they're charged so they don't need to be sealed away from sparks and humans, and you never need to add water. They're reputed to have better internal electrical characteristics as well, as far as discharging on their own and internal resistance and such. They do weigh more and cost more and have a little less capacity for their size, but AGM batteries are the state of the art and are awesome if you can afford them. They can also be shipped via UPS or FedEx, which would probably makes the price gap a little smaller by saving on freight charges. Again, a local battery store probably has them.
www.wholesalebatteriesdirect.com/solar-batteries/52513-12v-75-ah-group-24-deep-cycle-solar-battery-replaces-76ah-trojan-24-agm.htmlAnother budgeting option is to buy one small battery at a time as you can afford them, hooking them up in parallel, adding another 68 ah to your capacity with every one you add. Just make sure that each new battery is the same size as the others or it messes up their capacity and charging.
A 1000 watt generator (constant output, not maximum, meaning it would probably say it's a 1200 or more on the box, look for constant watts output if you buy one, so you know exactly what rate you can charge at) would be able to replace nearly everything the space heater used if you ran it for the same amout of time that you ran the 1000 watt heater. Thousand watts in pretty much equals thousand watts out.
You didn't mention whether you have a generator to take with you, but unless you buy a large battery, I think you're gonna need some way to recharge during anything more than an overnight trip. But you could just go buy a marine battery at Walmart (which again aren't very good for deep cycle applications like campers, despite saying "deep cycle" on them, they're simply lying), take it on a trip with the generator so that you can charge the battery if it runs out, and learn by doing whether that's enough for you or not. I was just trying to give you a more confident, accurate way to approach it. I hope this clarified it a bit more...