[quote name='Dead of Knight']I disagree with this post.[/QUOTE]
I agree with this disagreement.
I suppose it is the difference between those that merely enjoy the series compared to those that are truly fans of it. I am a fan of it and truly enjoy playing as one of my favorite, if not my favorite, character in the series. I may enjoy some cases more than others, but I have yet to encounter a case I have not liked.
Take Justice for All for example, I do not understand the hate it receives. Do I enjoy it as much as PW1 or 3? No. But being the worst Ace Attorney game still means I enjoyed it more than most other games. Like I said earlier though, I acknowledge that I am a bit biased in my appraisals.
Anyways, to answer the original question that was posed, I would most definitely start with the first Phoenix Wright game. At first, you may not see a connection between the cases and the characters, but the more you play, the more you will see how broad the scope is for the series story. The original trilogy should be played in order to appreciate it the most. Then I would move on to Apollo or Edgeworth.