Okay, here's the deal: if you've never read Ulysses before and want a quick and easy way in, Blamires is a great way to go. But be forwarned. While Blamires renders the story down to easily digestible bits, it is not (and I can't emphasize this enough) a substitute for reading Ulysses itself.
Perhaps the best approach (my approach at least) is to read a chapter of Blamires followed by the same chapter in Ulysses (others, I'm sure, will recommend Ulysses first followed by Blamires). Certainly, this constitutes reading two books at once, but it'll be worth it in the end. Another good source to begin with is Heffernan's Joyce's Ulysses, a four DVD set that can't, apparently, be purchased through Amazon. It is, however, available through The Teaching Company (a quick Google search will find the location, and no, this isn't a plug).
Now, both of the above sources focus on plot and character with virtually no emphasis given over to style (yeah, Yeats called Ulysses a book without style, but that's not really what he meant), and the provided analyses are at a very basic level. Interestingly enough, while Blamires shies away from the often raw sexuality of Ulysses, Heffernan positively laps it up. Further, given that Blamires provides us with an updated 1996 edition of his book, it's a little odd that he seems to miss certain elements of Ulysses that modern Joyce scholars have picked up on. For instance, is Stephen masturbating at the end of the Proteus episode? There is evidence to suggest that he is, but Blamires is silent. It is generally acknowledged that a fight ensues between Stephen and Buck Mulligan in the intervening period between the Oxen of the Sun episode and the Circe episode. Again, Blamires is silent.
Ah, but perhaps I'm treating Blamires unfairly because I did write above that his book was a quick and easy way into Ulysses. Besides, when explicating Ulysses, you don't want to give everything away (and even if you did, it would certainly take more pages than what could be found in a single volume). And so Blamires's book is deserving of its four stars because it is very good at what it purports to do (Heffernan is, I think, a little better).
Now that I've thoroughly offended you with my condescending and didactic prose, I shall in all likelihood offend you even more. Once you've read Ulysses, you'll want to read it again. During your first reading (along with Blamires of course), read it quickly, and don't worry too much if you can't understand the foreign languages or various biblical and mythical allusions.
There are three versions (well, editions really) of Ulysses: the original 1922 edition (Oxford), the 1961 revised edition (Penguin or Everyman), and the 1984 Gabler edition. I'd suggest starting the with 1961 revised edition as this is probably the cleanest (the Gabler edition has since become mired in controversy).
For your second reading, choose another edition and read it more slowly with a companion piece such as Thornton's Allusions in Ulysses, Gifford's Ulysses Annotated, or Gilbert's James Joyce's Ulysses - now you can take a closer look at those obcure allusions (but don't feel that you must look up every single one).
For your third reading, choose the edition you haven't yet read. At this point, you're ready to let Joyce's magnificent prose wash over you without the help of secondary sources. However, you're also prepared to approach the more scholarly literature if you wish. A journal like the James Joyce Quarterly can be a good place to start.
Of course, all of this begs the question: should Ulysses be read in conjunction with secondary sources in the first place? Ideally, no; realistically, yes. Ulysses constitutes a serious challenge for most readers, so secondary sources such as Blamires will certainly be helpful. By the same token, however, secondary sources can never replace the primary text.
N.B.: Since I believe in Karma, I'm sure I'll get my comeuppance for my oozing condescension in this review.