...Is it as simple as knowing how many amps a light or appliance or whatever uses/draws per hr and how many amps the battery can provide before needing to be recharged?
Yes, and Yes to your two questions.
Here are some things to know:
1. Amps times volts= watts.
2. Rearranging things, Watts divided by volts=amps.
3. A 12v amp is not the same as a 120v amp.
4. But, just because we like a challenge, Watts are watts. They're handy because they make it easy to compare a 12v gadget to a 120v gadget.
5. Manufacturers recommend for best life you don't discharge their batteries past 50%. That means if you have a new 80 amp hour battery, you should use no more than 40 amp hours before recharging.
6. As batteries age, they loose their capacity. But, I don't know a rule of thumb for how much per year. Probably because it depends on how you use the battery.
7. Inverters (changing 12v to 120v) are only about 90% efficient.
An 18 watt bulb uses 1.5 amps per hour. (18/18=1.5 See no. 2) Incandescent or fluorescent. Fluorescent bulbs seem to put out more light per watt, so frequently they can be less wattage and do the same job. So a 12 watt fluorescent might do the job of an 18 watt incandescent bulb. That's why fluorescents are handy for boondockers. They use fewer amps per given light level. Although some cause a hum in the radio. Some boondockers change their bulbs down in wattage to save electricity. Perhaps keep only one higher one for reading.
Use an 18 watt bulb for 3 hours and you've used up 4.5 amp-hours. Add up how long every gadget is on (in hours) in a given day and divide the battery capacity by the total you used and you have an estimate of battery life. Don't forget the water pump on and off, the fan over the stove, a radio or TV plugged into 12v, etc.
Wattage is pretty much in all in the bulb. I don't believe that the transformer in found in some flourecent lights
uses much electricity.
Running 120v gadgets through an inverter is a bear.
Although not a perfect analogy, I like to think of watts as work done. Imagine the work to be done is to toast two slices of bread. Let's pretend my toaster is a 1000 watt toaster. Lets pretend it takes 3 minutes to toast the bread. 3 minutes is 0.05 hours (3/60=0.05 hours)
Using big, beefy 120 volts that's 1000/120=8 amps(about) (no. 2 above). 8 amps x 0.05 hours is 1.2 amp hours.
You still need those 1000 watts (no. 4 above) if you're using wimpy, sissy 12 volts. With 12 volts you're using 80 amps (about)(1000/12v=80). 80 amps x 0.05 hours is 12 amp hours. Plus, you use about 10% more loss to the inverter efficiency (no. 7 above). That means you've used about 13 amp hours of your battery life.
80 amps drawn from your battery will need HUGE wires. I recommend you don't toast bread on an 120v toaster using a inverter!
When you see 12v appliances, they often are de-powered so they use fewer watts and therefore less amperage, but they take longer to do the job so the net effect is the same to your battery.
On the bottom or back of most gadgets is either the 120v amperage or the wattage. If necessary, convert the amps to wattage (no. 1) then divide by 12 to get the amps per hour from a battery. Add those into your total when calculating your daily usage.
More than you want to know but I got carried away. Mostly, what you suspect is true. The devil is in figuring out what you really use.