After Athenaze, you could try Rouse's A Greek Boy at Home
If you go to Ed Donnelly's page
, you'll find upwards of 30 “First Greek Reader”-type texts written for beginning students. I myself downloaded a dozen recommended by Spiphany
Once you feel you're up to an “intermediate” level, try some of Steadman's texts + commentary
. They're free to download, or pay for a hardcopy. If you want to try Anabasis, go for it! I'd recommend starting with an annotated reader's version - Ed Donnelly links to 5 different versions, and G. M. Edwards' version of Anabasis Book VI is available here on Textkit. (I also have Kelsey and Zeno's 1889 version of Books I-IV, but I can't remember where I found it.)
Hope this helps!