Do windows have one out yet?
Lol, yeah, Adobe Illustrator is the one you want - but use a lot of pencil and paper before touching the mouse. Work your ideas out etc. Don't build the house without the blueprints.
You would be committing a crime if you use Photoshop to do a logo and submit it to your client as a JPEG file. Web logo, print logo or whatever, it should be scalable (ie vector). It is alright to present ideas in photoshop, paper n pen or what not, but never finalize a logo in it. What would happen if suddenly your web client asks you to submit a logo vector?
If you make changes in illustrator, always keep a duplicate copy of each changes you make in case you want to roll back to your older ideas. You do not have to create 20 files. You can work on drafting your ideas in a single file.