Final Fantasy I is not the fanciest RPG on the PSP, but it's solid, old-school, fun, and a great portable game.
Visuals: There is the odd cut-scene, rendered in the usual Square Enix glory, and they look great on the PSP. The in-game graphics, however, are VERY "traditional" in that it looks like the most gorgeous Gameboy Advanced title you've ever seen -- the characters are barely more than mobile, lightly animated icons. The scenery is all cookie-cutter tile-based patterns painted on the ground in 2d. Your character slides around the screen in a more Ultima III style way than a Final Fantasy VII way. That said, everything is detailed nicely (in a cartoon style), and the color palette is bright and fun.
Audio: As with most Square titles, the orchestral soundtrack is fantastic, and really elevates the whole experience. There are no voice-overs, so you'll be reading your dialog (which thankfully isn't a lot). Sound effects are again more like a GBA title -- sparse and not exactly exciting.
Gameplay: This is straight-up circa 1990 RPG gameplay. Truly turn-based combat (which makes for a terrific portable gaming experience -- if you're distracted by the real world during combat, you're not going to get slaughtered as combat carries on without you), a large though very generic looking gameworld. Everything looks and feels tile-based -- you move about the grid either on the world map level, or within a town or dungeon. Combat is difficult unless you take the time to "level grind" by fighting lots of random battles in each area to get your characters buffed up.
As for the RPG elements, stats are automatically incremented when you level up, there are only a few classes, but there's a decent variety of spells and weapons/armor to select from. The story is extremely cookie cutter -- save the king's daughter... The dialog is all very short and reminds you of many other old console RPGs -- short and sweet.
While this all makes the game sound weak and useless, it actually is a perfect combo for the PSP. For portable gaming, you never know when or where you'll have time to game, and a deep, complex RPG can be hard to play in short bursts. But an RPG like FF I is just the right depth, and is a lot of fun, to pick up and put down frequently.