When I first started using my CPAP I had to have oxygen with it. If I was traveling I just went without the oxygen and used the CPAP by itself.
Now for some encouraging news... after using the CPAP and oxygen for a couple years I was reevaluated by my doctor and they found that I no longer needed the oxygen. My doctor said it's not uncommon for the body to adjust after continual CPAP use and O2 levels go up. I was really happy because even with my insurance I was paying a lot of money for the O2 and it was loud at night.
My advice, make sure that you're going to see a sleep specialist and going for yearly check ups. When I was first diagnosed, my primary care doctor felt like he could handle this himself and essentially just sent me home with the CPAP and O2 set up with no follow up or anything. If I hadn't moved to a new area and started seeing an actual sleep specialist, I would probably still be using that oxygen.