Photoshop :: Detailed Vector Images From A Photo?

I have an image of 4 greyhounds, and i want to vectorize them in high detail so i can use it within a logo for a web project. The image is: http://www.valkama.org/blog/uploaded...ama-739767.jpg

I have been using photoshop for a good year or 2 and have used the vector tools to create a number of vector images but nothing as detailed as this.

If someone could answer the questions below and maybe offer some personal advice that would be great:

1 - Would it be better to use a package designed for vectoring rather then using photoshop. I heard from a few people that Photoshop isn't the best tool for the job.

2 - How long would something like this take? A few hours? A day? Like i said i havn't done anything like this before even though i worked as a graphic designer for 8 months.

3 - Where would i start? Im thinking start with the dogs bodies, them move onto the coats (the coat with the number on it) etc etc, leaving the fine detail till last.