I don't think there is a specific DAW which is best for ambient. What one person finds best for them isn't neccessarily going to be best for you. I think it needs to meet your requirements of how you want to work and what you want it to do for you, so it is what is best for you to enable you to have a positive workflow.
I am only experienced with Cubase and I find it great for me and the way I work. Of the others you mention, I believe Reason is a self contained programme, that being you can't use third party VSTi or plug ins. Althought you can use it with a DAW using the Rewire function I believe.
From what I hear about Live, isn't it more loop based, as for the others, Logic and FL, I know nothing about these.
I would say get yourself a good keyboard controller with plenty of knobs to tweak the controls on your vsti, Novation do some good ones, and Akai have just released some new ones. I would use a seperate controller for DAW control and mixing, something like the Novation SL mk2, or similar. If you intend to record stuff to release, you will need an audio interface, to get the best possible sound recorded, there are many of those to choose from, Tascam, Focusrite, Presonus, M- Audio, to name a few, all make audio interfaces.
PC or Mac, each to there own, I suppose each has it's advantages and disadvantages, boils down to personal preference. I use PC, don't think I would change to a Mac now, And I never use my music computer on the internet.
It would be nice to know what you end up with, but most important of all is that you enjoy creating with the tools you have chosen, oh and welcome to the forum