What do you mean stand alone?
The way the show works is that there is a main mystery thru the whole season....and individual mysteries each episode. And along the way there might be a second major mystery that helps with the investigation of the first main mystery. I hope that wasn't too confusing.
Here's a layout---
Season 1 revolves around the murder of Veronica's best friend. That is the big mystery. Amongst that mystery you have the mystery of the week for each episode.
Season 2 revolves around 2 major mysteries. The first being what did Logan Echols really do that night......and the second mystery appears at the end of the first episode of Season 2.
Season 3 shows Veronica starting college. This time they flip the format a bit and we get "arcs". There are 3 mysteries....but instead of them overlapping like the previous 2 seasons....each of the 3 big mysteries are presented in arc format. You get the mystery of the week of course...but you have the major mystery. Once the first major mystery is solved....another major one pops up.....then once that is concluded....you get the next.
I'm gonna be truthful here TOG. I honestly think you'd like it. Despite it being aired along with Gilmore Girls...this show is not girlish. It is genuinely awesome.