I recently took the Math GRE subject test and found it quite challenging. My recommendation is that you do as many problems as you can, as quickly as you can. I recommend placing emphasis on calculus first, as it takes up 50% of the exam, then linear algebra/abstract algebra and then the other topics.
I have never used Apostol's book but here are my first impressions (bare in mind I started looking at it 5 minutes ago). It contains the standard material that is assessed in the GRE, this makes it useful for brushing up on any things you may have forgotten or misunderstood. It also seems like there are quite a lot of exercises but a lot look like standard computational exercises.
You need to be able to do these type of questions, but don't expect them to come up the GRE. The questions in the GRE are more complicated and require a deeper familiarity with the material than basic calculations. I would recommend taking a selection of exercises from a variety of sources: do some basic computations from Apostol and make sure you can do them quickly and accurately.
Then try to find harder exercises, maybe some of these can be found in Apostol or try a different calculus textbook like Stewart or Spivak. Then try to look at some hard problems; aside from previous GRE's, the best sources I can come up with right now are the "Berkley Problems in Mathematics" books but they are definitely above the level of the GRE (but hey, who doesnt like looking at hard math problems!).