I don't know the chronological or canon of the series myself. It's a long and a bit confusing one for me. Tho I guess it's safe to start on the PSP. Just know the Trails in the Sky or TITS(yes we know the joke) is a very text heavy game. No seriously. The second TITS game contains so much text it takes two PSP UMD's. Why it's still in Japan ATM. In time we can only hope XSEED or someone can bring the rest of the series over eventually. Or if you speak Japanese you can play a couple of the games on Japanese PSN.
It had humble beginnings.
From this
To this
Now like all Falcom games the music will be fast paced rock heavy and energetic. Also very anime looking so if that's not your thing then might not be your series. Unlike some JRPG's over the last few years Falcom never apologizes for being very classic Japanese styled games but they do make it work and do change things up as well to keep it interesting.
Next month I plan to get TITS on PSP along with the OST.