There was no awful FF game released during the PS1-era, so commence in playing any that you haven't already finished. I'll recommend FF Tactics in addition to FF Chronicles and FF Anthology, because I'm sure you've played everything else. Despite the power of FF6 that Anthology holds (with FF5 rounding out the package), Chronicles is probably the better deal in the form of Chrono Trigger and FF4. The only one I wouldn't recommend is FF Origins. I didn't have too much trouble with FF2, but it seems that most players experience more frustration than fun with this game. That, and I think FF1 is better experienced with 8-bit graphics.

I don't know if you'll have much luck finding them, but both the Complete versions of Lunar 1 and 2 will provide you with much enjoyment. Lunar 2 is more difficult, and will make you feel like a man if you finish it (I smoked a cigarette upon seeing the ending credits, and I don't smoke); Lunar: SSS has a better story and is more fun overall. Both are very long, though, and will as such hold your attention for a while.

Brave Fencer Musashi. Forgettable story and intentionally cheesy dialogue and themes aside, Musashi has shown me a good time. It'd be best defined as an Action/RPG with more emphasis on action and exploration, and not so much focus on the RPG aspect (I doubt you'll ever find yourself fighting to level up). The Fusion Assimilation system, the powers gained from scrolls, and learning new moves and finding Legendary equipment by means of rescuing villagers from various locations and dungeons are what set Musashi apart.

Other titles that I had a lot of fun with but wouldn't necessarily recommend to everyone:

Legend of Legaia. Legaia's unique battle system is both it's biggest advantage and disadvantage. It's pretty nifty, and will lead to many hours of experimentation in hopes of finding new moves and move combinations (unless, of course, you use a moves list FAQ or something), but random battles can become tedious in later parts of the game as the monotony of each encounter presents itself. I personally like battle systems that are quick and simple instead of ones that offer more depth and give you battles that are five minutes long, but fighting -and specifically, boss fighting- in Legaia am goal for me. The boss fights in this game are some of the most epic and memorable that I've experienced. Not everyone likes it, but there are those who love it.

I had another one in mind, but I forgot. I'd try to remember, but I just bought Tales of Symphonia, and it's calling my name. Oh wait, it was Breath of Fire III.