It's important to know right off that Mario Party has nothing at all to offer solo players. That might seem obvious from the title, but sometimes these party-focused games also have enough of a single-player mode to be substantial (i.e. Super Smash Bros. Melee). Not this one, though. You *can* play single-player, but it's against robotically perfect computer opponents who crush all the mini-games even on Easy mode. You also have to watch them do all their boring little single-player games too.
The mini-games are done in an intentionally slippery style to promote yelling and craziness at group gatherings. Of course, for single-player, that just puts you at a disadvantage against Robo-Computer. There's no way to practice them initially outside of the main game, either -- you have to buy them individually by, you guessed it, winning games. That process can take absolutely forever.
There's actually a pretty significant time investment and learning curve for something that's supposed to be an ultra-casual game, at least if you want to get good at it. The best way to play it is with 4 people who all suck at it. If anyone actually sinks the time in and masters the mini-games, they'll stomp all over everyone else.
Mario Party also turned out to be a lot darker than I expected. Failure at mini-games usually means a grim death for the losers. From drowning and having your carcass carried off to be eaten by Bloopers, to murdering the other three players by dragging them into a Sarlac-like piranha plant pit, to a gangbang by malicious ghosts, I wouldn't be surprised if some little kids were traumatized by this game.
Strictly as a party game, it's actually held up pretty decently as far as play control/concept, and even in terms of looks (if you don't get snobbish about blocky character models). I haven't played any of the sequels at this point, but I'd imagine it's been surpassed by at least a few of them, however. So there might not be much point unless you can get if for cheap for an actual N64 that you leave hooked up for parties, or if the newer Nintendo consoles have a downloadable version for a low price.