if you have a 3ds, the whole trilogy is available to download for less than you'd think. Phoenix v Layton was a fantastic game, though I'm not as much a fan of the Layton stuff. The court stuff more than makes up for it though. Dual Destinies was a crazy hoot. I stayed up late most nights while playing that because I wanted so hard to know what happened next. It's been long enough since I've played AA4, hopefully I've forgotten some of the plot threads and can experience them fresh-ish.
The neat thing about Phoenix/Layton is you really don't need any backstory apart from the tiny amount of info from the 1st and second game (Hey, Maya exists!. Hey, the Magatama exists!) Other than that, it's a straight up side side story