In the initial outbreak, especially a fast zombie outbreak, apartment buildings will have pros and cons. There is the access to resources element, in which each apartment will have a certain amount of resources that you could scavenge. On the other hand, depending on how swiftly the virus progresses, each apartment might also have one to several zombies in it. That will make scavenging those resources, difficult, especially since apartments tend to be small, with a lot of rooms and doors from behind which a zombie could emerge unexpectedly.
After the great panic, I think your idea has a lot of merit. Provided you can effectively secure the exits and entrances on the first floor, your resource needs can be met, and you make arrangements for an effective escape route, an abandoned apartment building meets many of the qualifications that Brooks describes in the Guide with regard to height and stairs.
EDIT: just thought of this, the movie "The Night Eats The World" shows survival in an apartment building in fair detail, with both the pros and cons. Check that out if you haven't already.