Get Vigilante 8 and Vigilante 8 2nd Offense. Car combat GOAT's that deserved much more attention.

And don't you DARE skip MGS1 for The Twin Snakes! This is pure gaming blasphemy.

My top recommendation is Revelations: Persona (Persona 1). Though you might want to go with the PSP remake instead.
Dragon Quest VII aka Dragon Warrior VII is another top RPG.
On Final Fantasy, since there's no connected story you can play them in any order. And I'd recommend starting with FF9 before 7&8 (especially if you've played any of 1-6).

Gran Turismo 1 is the best driving game I've played. But Ridge Racer Type 4 had great feel of drifting.

Echo Night is an interesting little horror adventure. But unless you have much more patience than me, you'll want to have walkthrough at hand.

About Clock Tower: the naming of the games is a mess. There's original SNes Clock Tower (recently remade), then Japanese CT2 for PS1, called just Clock Tower in the west. Then third game, in Japan CT: Ghost Head, in the west CT2: Struggle Within. And finally a PS1 remake of the original as CT: The First Fear.
So the order is (by western names): First Fear (or play the modern remake CT: Rewind), then PS1 Clock Tower and finally CT2: Struggle Within.
However, while the second game is direct sequel to first, CT2: Struggle Within/CT Ghost Head is entirely unrelated. I'd also say it's the worst of the games.

Soccer is a rather specific taste, but I have to mention LiberoGrande, a bit different sports game.

Legacy of Kain Soul Reaver is an essential experience, but there is a good quality remake available on current consoles, so it comes down to whether you want the original experience, or a modern makeover.

Legacy of Kain and a lot of other games got excellent DC ports. A Dreamcast with a GDemu would help OP a lot. 

My friend, you cant ask this question about the PS1. There is just too much to recommend. In 10 minutes I could list over 100 games.