I'm SuperbowserX. That is my name on other wikis out there, but my name on YouTube/Bulbapedia is Subscriber0101.
(Note: Much of this page is a memento for myself).
How I got into the series? Well there is this reviewer out there called Wiiviewr, and I saw his review of the first 2 Wii ports. Some months afterwards in early February 2013 (around 5th-10th to the 24th) I then got into playing the first DS game and was HOOKED. Eventually, while I was playing Rise from the Ashes I just converted to the Wiiware version and played through the whole game again on that and beat Rise from the Ashes (March 9th). Then, I began going through the PWAA2 (March 9th - Early April) and PWAA3 (April 6th- May 12th) games on Wiiware in. By June 24th I managed to entirely beat Apollo Justice. Also, after a long break from the series (I kind of overdosed/over-fanboyed on it), I beat MEI (started Jan 2014, wrapped up May 25th 2014, but my system broke halfway through that point).
Then there was the unofficial port of Gyakuten Kenji 2 which I wrapped up over the course of June-July 2014. Even though it's a little bit illegitimate a nominee since much of the text had to be translated arbitrarily (for of course a perfect translation would actually not make clear sense), the game tops the other Ace Attorney games as my favorite.
Fortunately, I am able to play Dual Destinies on my iOS device now. Going through it atm.
From favorite to least favorite, that's GK2, PWAA3, MEI, PWAA, PWAA2 and AJAA.
Here are a fav-to-least-fav list of cases for each game IMO.
Ace Attorney Investigations: Miles Edgeworth: The Kidnapped Turnabout, Turnabout Airlines, Turnabout Ablaze, Turnabout Visitor, Turnabout Reminiscence (Favorite Track: Tie between Lying Coldly and Presto 2009)
Gyakuten Kenji 2: The Grand Turnabout, The Forgotten Turnabout, Turnabout Target, The Inherited Turnabout, The Inherited Turnabout (Favorite Track: Tie between "Allegro" and "Investigation Middlegame").
Good luck, and happy solving!