I would recommend that you try to operate the CPAP off of the inverter (hook it directly to a car's battery) before you go looking into buying large amounts of batteries. There are some things that just don't like "modified-sine" (more like modified-square!) waveforms. If it works for you, plan on having at least 12AH of battery power for every 1 amp your 120V appliance draws.
This adds up really quickly:
For the below, we'll be using the most commonly available battery suited for the load, a group 27, typically available almost anywhere, ranging in average price from $75-120 or so.
Your average group 27 size marine/rv/deep cycle trolling battery can provide about 80AH of it's 100AH rating before you hit the point where the voltage really sags. So if you are using 1A/120V, count on the inverter pulling at least 11-12 amps. At that rate, your battery would be dead in a little over 6 hours. So, you would need 2 batteries to get through one night.
Now for the fun part: charging!
The easiest way to charge this back up would be to jumper-cable it to your car (don't forget about all the safety issues this can bring up). Also keep in mind that the below figures take into account the fact that vehicle alternators do not put out anything near their full power at idle speeds.
We'll continue to assume that your load used 12AH for 8 hours, for a total of 96AH.
Your typical vehicle's charging system has about 10A or so of charging capacity at idle, with all the vehicle accessories (lights, wipers, fan, etc) turned off. So with that easy numnber, we can count on about 10 hours (and probably close to 1/2 a tank of gas) to recharge the batteries. If we are revving up the engine (to about 2000-2500 rpm), we can get more output from the alternator, which would give us maybe 40A tops available. This would still take 2 1/2 hours to charge and still use a lot of gas.
If you want to use one of the little Honda generators to charge a battery, plan on running it all day, their DC output is only 8A.
The best plan, in either case, is a small generator, like Turbodog recommended. I too would recommend the Honda, although for the money, I would go for the EU2000. Twice the output power, bigger fuel tank, can be paralleled for 220V rigs (lots of RV'ers do this!), and is only about $250 more. You can always use it for other things, such as construction work and power outages. Oh, and even the EU2000 is lighter than just 1 group 27 lead brick... /ubbthreads/images/graemlins/grin.gif
Just my observations, suggestions, and opinions!
Chris