The Basics: An inverter takes a power source such as a 12 volt car battery and converts it to 120 volts to power such things as
cell phone chargers, laptop chargers, and small table lamps. You can parallel (2) 12 volt batteries to give you more hours of use
before needing to recharge with generator or hook up via solar panels.
There are plenty of you tube videos describing how to parallel batteries together, but even one battery is good.

First thing is the larger the inverter you buy, the more things you can run.
However, the more things you run, the faster you'll deplete your 12 volt batteries.

What can I run? The basic use of an inverter is to power the things you really need. Not what you want but what you need.
You're going to have to compromise on just what these items are. Forget such things as refrigerators or A/C units.
You'd need a huge number of batteries to do that. Stick to your basic needs only.
If you positively need refrigeration for such things as insulin, This Item or This Item might work as only draws 50 watts.
If you do go this route, connect unit directly to batteries as more efficient than thru the inverter.

Types of inverters.
There are two basic types of inverters. Modified Sine Wave and Pure Sign wave.
Pure sign is more expensive but the better choice for powering items that may not work with modified sign wave.
Examples of items that may have issues with a Modified Sine Wave inverter.
Televisions, microwaves, electronic clocks, or anything that has digital displays. Some items such as microwaves
may still work but will draw more power than they normally would.
If your budget allows, always go with Pure Sign wave inverters.

A real world example from my experience with Hurricane Irma and no power for 8 days.
I had two 12 volt deep cycle marine batteries. Nothing fancy at all and I already had them.
I was using a Potek 750 watt inverter which I've listed in my Amazon links. Modified Sign Wave version.
The reason I love this inverter is it tells you the condition of your battery and also how much power you're actually using.
I had installed 8 watt LED bulbs in 2 table lamps. (Same light as normal 60 watt bulbs)
I still had internet for some reason so I was charging my laptop and cell phone.
I also monitored my ham radio from time to time. If you're just listening, takes very little power.
I also used a 400 watt rice cooker from time to time. I even ran my TV or radio for local news for short periods.
The end result was I never had to recharge my batteries during the 8 days with no power.
The key is to know how much power you really need for such things as CPAP machines and size the inverter to match.

A really cool item to have is a basic watt meter to test what your items are really consuming in power.
Just plug the watt meter into the wall and then plug your appliance into it to get it's power use in watts.
Add each individual item's power consumption together to get the size inverter you'll need in watts.
You can use a smaller inverter than the total watts figured but you won't be able to run everything at the same time.
The Potek I've listed is NOT pure sign wave but seemed to work with everything I was using.

and able to be discharged to a lower voltage and still take a charge.
AGM batteries are even better but need a special charger. I don't recommend.
If you are starting from scratch, buy two new batteries with the same amp hours of capacity. If that is not in your budget,
use batteries of the same size. Hooked up in parallel, using similar sizes, their charge rate will be about the same.
Don't forget to keep the batteries outside at all times. Especially during charging.