I never played any FF other than FF VIII. I do think FF VIII is a great game, but it doesn't really work in the PS1 because it is too advanced for the console. I mean, the game had beautiful graphics, story and soundtrack. However, the PS1 didn't let the game shine. I'd like to see a remake of that FF for the new generation platforms. I think RE2 is more entertaining than FF VIII overall, although FF VIII is a greater game.
I never played any other FF, but every FF has a separate story so you don't need to play every FF before playing a new one.
FF VIII (and I guess VII too) is a RPG game, the battle system is basically turn-based fights, but it's very complex. For example, you need to combine your moves (Attacks) to a certain type of magic so you have better attacks, and you also need to think which magics are better for the enemies you are expecting to face. You also have to associate characters to Guardian Forces, which are God-like creatures, in order for them to be able to use magic. The Guardian Forces learn new abilities that you can use to become stronger, and you can also summon them during fights in order to help you out with your enemies (though this is only useful at the beginning of the game).