I used Dobson's book early on. Nice, gentle introduction.
The best assessment (for the beginner) of various Greek books I have found is on this webpage: http://www.pocm.info/good_books_read_greek.htm
Scroll about halfway down the page and read carefully the comments about the pros and cons of Dobson's method and what you need to do to rectify the problem.
I would highly recommend Dobson's fun and welcoming book to get you started, but I think most people will begin to feel lost in his highly inductive method by chapter 15. I didn't even make it as far as the POCM website said I would.
I did what was recommended and purchased Mounce at that point. Mounce has a great, approachable grammar method for the beginner. But readings and exercises are only found in his workbook, which I personally found to be useless. Unlike Dobson, Mounce's workbook quotes bible verses you will already know. The verses/quotations you read will be bulked up with many repetitive phrases that run through the NT, like "of Jesus Christ our Lord", a phrase you only need to read a handful of times in the course of the textbook to know. The workbook for me involved recognizing a verse or verse theme I already knew and then "reading" it. Hopefully Mounce will revise the workbook, buff up the vocabulary and write some original sentences and stories for it. Not to mention putting an answer key in the book.
If you follow the POCM website's advice, you will return to Dobson after learning grammar from Mounce. I sort of did that. But at some point, I got fed up with going back and forth, trying to find places where Dobson's book would give me corresponding reading practice for Mounce's grammar. Nor can you learn vocabulary effectively in this scattershot way. If Mounce and Dobson (now sadly deceased) had gotten together, they could have created a really meaningful package for learning biblical Greek.
So I ended up buying Athenaze I, some of which, at that point, was review. After finishing Athenaze I, I went through the "Summer Greek Reader" (with passages from the NT) and found I had very little problem with it. Since I'm learning Greek for kicks, and not as a seminarian or bible student, Athenaze has turned out to be a good fit for me.
I'm still glad I began learning grammar with Mounce, and without Dobson, I would have quickly quit learning Greek altogether. My advice is to use Dobson, see if you are motivated enough to stick with it for 15 chapters, and, if you are, start looking for other books to supplement or continue with.