Yes, 1 & 2 Chronicles for the PSP is a great port. Being 2D sprite-based makes it a sharp, vibrant and visually appealing on both the PSP and Vita.
Oath in Felghana should definitely be experienced on PC, though. The resolution, 60 fps, and being able to use a comfortable controller of you choice trumps the portability, VAs, and other extras the PSP game brings (not to mention the smeared visuals, yuck).
Origins is obviously only available on PC.
Even though Origins is the pequel you should definitely play 1 > 2 > Felghana > Origin in this order. Not only will you be more accustomed with the (lite) lore and characters this way, but you'll experience the series evolution and appreciate it more visually and mechanically. I also hope you dig good videogame music because your ears will be like OMGGG DUUUUDE~
My overall impression is that I should have played these games a long time ago, it's just something that's been missing from gaming life. I really regret not playing Ark of Napishtim (VI) when I had the chance, and I really hope it gets released either on Steam or PSN, as the PSP port (available on PSN) is trash, iirc.