Hi Paul, I had CFS for two years when I was younger and just wished to say well done for beginning to feel that you're beating it. Its extremely hard work, especially as its an illness that many people just don't get.
I would like to say I exercise like a demon now, but I don't and I can't, even though I recovered many years ago. I found the one exercise that allowed me to build up my strength gradually was swimming. I started to swim gently for three-four days a week and also took some private lessons to ensure I was doing it properly, which made a huge difference. In addition to this I walked a great deal - everywhere in fact! Once I began to feel more human I then added some gentle gym work and cycling to the mix, plus I have dogs and walk them daily for at least 30 minutes - they are a great motivator although I appreciate not everyone can have them.
I'm not an expert in this subject at all and it maybe that a trainer may be able to give you some more specific advice about your particular case. Take it slow, don't get frustrated and just enjoy what you do. I have to be careful because I burn out very easily if I overdo things (especially alcohol! But it is sooo nice!). But it will get easier. Feel free to contact me if you want to talk anymore.