SLR Zoom Lens Depth-of-Field?

1. no 2. a cheap zoom to discover what you really want.

Even if you were talking of fixed maximum aperture (like f/2.8) the DOF won't remain the same because as you zoom you are magnifying the subject and that would effect the DOF. (leaving a link on dof..) As for the first lens (presuming that you missed out on the kit lens) you can start with a 18-55mm or 18-105mm zoom.

Regarding depth of field, probably not. However, I'm not sure how you could tell for sure unless you did the proper math according to optical principles. You lens will have a maximum aperture of f/5.6 at the telephoto end and f/3.5 at the wide end. As the focal length increases, the practical depth of field narrows. However, because a small aperture has more depth of field, you have two mechanisms working against each other. It's the opposite effect at the wide focal length. You can have a wider aperture, which gives you less depth of field, but wide angle lenses by virtue of their short focal length have a wider depth of field. As for a first lens, a 50mm will force you to step forward and backward in order to frame your shot. It will also make it more difficult to get everybody in the shot if you take a picture of a group in a small room. However f/1.8 is a fast lens. So it will be helpful in low light situations. It will also have a narrower depth of field at f/1.8, which contributes to blurry backgrounds. Your choice.