I wanna go back and play P1 PSP again one of these days. Probably should give P2's twin games a go too. P1 particularly though because back when I owned the UMD the Snow Queen quest kicked my rear. Badly enough that I lost interest in the game as a whole. Very much want to defeat that challenge.
Some advice for anyone who does decide to tackle the snow queen quest:
There is this bullshit mechanic that if you want to get everyone's ultimate persona you need to do the dungeons in the reverse difficulty order (i.e. you must do Thanatos, the most grueling dungeon first. In this dungeon, if a character dies in battle, their persona get sealed away, and you need to backtrack quite bit to reclaim it, wasting potentially precious time.). Unless you have absurdly completionist tendencies, I would not advice attempting that. It means you need to hours of grinding and messing with the casino as preparation at the beginning of the game, and it completely breaks the balance of the rest of the game. If you do the dungeons in the "normal" order, the Snow Queen quest is not that hard, though the fact that you cannot save for long stretches at a time and you are under a time-limit can make it rather frustrating and unenjoyable.
The Lilim persona that can be fused early in the game is completely broken, and makes the final boss a total joke.
Over-all the game really hasn't aged well, and if people are looking for something like persona 3/4, they really ought to look elsewhere. Not just because of the lack of social links, but the gameplay really doesn't have that much in common.
The battle system is slow and at times clunky, there is one dungeon that you need to run through 3 times in a row to beat and there is a really annoying and poorly balanced dungeon where you only have 2 party members, which doesn't work well with the way battles play out. The story and characters are also pretty unmemorable and I hated the ending.
However, the dungeon crawling is well-done, battle system does have some enjoyable and interesting quirks, and code breaker (a sudoku-like mini-game) is REALLY addictive.
So in conclusion:
The links to persona 2 aren't really substantial enough to make playing persona 1 necessary for its enjoyment. If you are itching for a somewhat old-fashioned dungeon crawler, you may still be satisfied with the game, but otherwise skipping it shouldn't be a problem. Though if you are looking for that sort of thing, I personally think strange journey is a better game.