There are a number of competing criteria: max number of books, min cost (which may involve owning some books already), max depth of coverage, max breadth of coverage, max quality of writing for your level of expertise (this one is complex),... all with varying degrees of dependence.
Rosen (the discrete math text) is growing by committee in the classic commercial math text book style (adding more and more sections and history and examples and subareas) in order to be -the- text book, so that you wouldn't need any others. I personally feel this is part of the textbook publisher thrashing scheme to pull money out of students. The book may be good and constantly getting 'better', but has that general 'bloating' feel to it.
I think you can decide for yourself on a first pass the coverage of the two cheaper books against Rosen (or between any two adversarial choices) by comparing their table of contents (Rosen's is not on Amazon but directly through the publisher mhhe.com). I have used Rosen and like it for readability/I have heard that students don't care for it; I have never used Anderson or Lovasz (Lovasz's advanced books are excellent). Rosen seems geared towards CS; both Anderson and Lovasz touch on finite fields/designs which Rosen ignores altogether (but Anderson spends 1/4 of his text on it).