...buy Professor Layton and the Unwound Future without playing the other ones? I do care about the story, this one is the cheapest at my retailer though, and it will determine whether I buy the other ones. So, Could (or should) I?

I wouldn't. You should play Curious Village first to get to know the characters.

I would say the Layton games are best played in order. You're not missing much if you skip over Diabolical Box, but you'll still be missing a few things if you skip that and play Unwound Future instead.

Curious Village absolutely must be played first.

This, or at least read the plot summaries and such on Wikipedia.

It'd be best to start from Curious Village like the others said, just to get to know the game and its characters. I haven't beaten it myself actually, I couldn't take doing puzzles every 5 seconds. But like any series with a story, they're best played in chronological order.

Aaaaaand I just checked, Curious Village is a tad bit cheaper, so I'll probably get that. Thanks for all the feedback, everyone.

Sure thing bro. You'll be hooked into the series before long. Prepare you wallet.

this series is awful, dont buy it. (IMO) I guess I'm just too stupid to like the music, and to understand the dang puzzles.