Survivorman,
You need to look into the 12-volt ratings of your CPAP machine. I looked for 12V power specs for a Resmed CPAP, but there are numerous models and I wouldn't want to make assumptions on your exact requirements. Several that I saw appeared to need 150 watts (please check your specific requirements) so I'll use that as an example. 150 watts at 12V requires about 12.5 Amps minimum. (Watts / Volts = Amps) - Remember that is the absolute minimum.
The wire, the 12-volt outlet, and the fuse all need to be sized to handle the maximum load expected. Oversizing the circuit provides added safety, and probably at only a minimal cost. You obviously need the fuse to be sized less than that of the current rating of the wire and outlet. That's what fuses do - they protect the circuit from overload.
I've pasted a section of one wire sizing chart. This chart is for use on "short runs" and with no other considerations. If you are looking at a wire length over 10' to 15' or higher ambient temperatures (like in the basement??) you probably need to increase the wiring by one wire size.
AWG 12V
22..... 5A
20..... 8A
18..... 10A
16..... 20A
14..... 40A
12..... 60A
Obviously, there is no 12 volt wire size for exactly 12.5 Amps, so you have to go to the next larger size wire to prevent from being overloaded. That would mandate a 20 amp, 16 AWG circuit, and probably a 15 Amp fuse to be safe.
The other school of thought is that you (or someone) might want to use that outlet for some other 12vdc appliance one day, so you may want to run the maximum circuit that is practical. It might (or might not) cost you a little bit more up front, but allow for some added flexibility down the road. Find the appropriate 12 volt outlet that matches the physical requirements of your appliance (assume a typical cigarette lighter plug) and your mounting constraints, etc. Insure that that plug exceeds the electrical requirements of your load and then size the circuit to the max rating of that plug's capability.
Example: If the 12 volt plug is rated at 20 amps max (pretty standard, but you have to check), I'd size the wire for 20 amps (16AWG) minimum. Since the difference in wire cost is negligible, I'd up size it to 14AWG and fuse it at the full 20 Amp capacity. This would provide plenty of "cushion" and at very little extra cost.
I Hope this helps.