(For reference, the correct play order is Legacy - Unbound - Convergence - Deception - Epiphany. The series pretty much plays like 5 chapters of a single game, so this review is the same for each.)
You play Rosa Blackwell, who much to her annoyance has inherited the family spirit guide- Joey Mallone, a 1930's gangster type who absolutely insists she spends her evenings resolving supernatural oddities by calming the ghosts causing them and helping them move on to the next world. Of course, only Rosa can see and talk to these ghosts, so traipsing around New York apparently talking to herself is the order of the day.
Right off the bat, Blackwell is sure to evoke nostalgia in those of us who played adventure games back in the day. Remove the voice acting and you could convince me these were hidden Amiga gems that were recently unearthed. The pixel art changes in style between each game but is always crisp, clear, and remarkably detailed- some animations are a little choppy but that's kinda nostalgic too.
The games are easily comparable to the Phoenix Wright titles, and I'd say anyone who enjoyed those will have a good time here. The focus is much more on the story than the puzzles, which usually involve gathering information from the right places and using it to help the ghosts realise their time in the mortal world is over. It rarely falls into the adventure game traps of obtuse puzzles that make no real sense, and the times it does are almost entirely in the first game- in-game commentary from the developer notes that he's well aware of these early stumbles and actively avoided them later.
Probably the point that will discourage those who watched the trailer is the voice acting, which early on is admittedly amateur and clearly done on home hardware rather than in a studio. Please, PLEASE do not let that turn you off the series. If it's a dealbreaker you can turn voice acting off completely in each game, and after the first two games it gets markedly better. I was unsure on Abe Goldfarb's performance as Joey to begin with, but by the end of the series I couldn't imagine anyone else in the role. Just.... Just weather the storm and it'll pay off later, trust me.
All told you're looking at 15-20 hours for the five games (though that depends a lot on how good you are with solving the mysteries) and achievement hunters will play through each one twice, though the second time through is a lot quicker. I became very attached to Rosa and Joey in my time with them and I'll miss them now their adventure is over.