You're entirely welcome!
I don't think there's anything better than Ai for logo design, but that's just my opinion. I preferred Corel Draw until about 2003, and then Ai pulled ahead and hasn't stopped improving.
Be sure to explore File > Save For Web to see the various output options. But there are so many ways to approach designingweb elements in Ai that I couldn't begin to cover them here.
The beauty of designing in vector and outputting as PNG or JPG or GIF (for example) is that you can produce any scale of output you might need without changing the original design. (When the output is very tiny, of course, such as a favicon, then you might be better off designing with individual pixels (and I'd do that in Photoshop), but I'd still start with an Ai design, output to a tiny bitmap, and then tweak it dot by dot in Photoshop.)
Happy designing!
Allen