Fantastic series.
AA1, for me at least, is probably the best in the series, mainly due to how new all of it feels. The latter games are also great, but the series does end up repeating a few tropes. Case 1-3 never really felt like a filler cast to me, whereas the 3rd case in other games usually is.
AA2 is a slight drop, mainly because of 2-3. But AA3, holy shit, that story. 3-4 had me afraid to be alone in the dark at night. That scarred me for a while. And yeah it all comes to a head in 3-5.
It's weird to say, but even though Apollo Justice AA is my least favorite game in the series, Apollo Justice is my favorite character. It's one and done, but it necessary to play for future games in the series.
AA5 was a good return to form. Haven't finished AA6, but I am enjoying it more than 5. But I am on a pretty obvious filler case so I'm not that motivated to go back right now.
Try not to burn through the entire series, feel free to play something else in between AAs.
But yeah, cases 1-2, 1-5, 3-4, 3-5 are the best in the series.