Anyone who has read my thought on SMA3/YI and the later Mario Party games should already know my opinion. I, personally, think that SMA3 has a lot more replay value, maybe unless you've never played any Mario Party game at all, but if that's the case I'd tell you to get a copy of the original N64 Mario Party.
To address your questions: Yoshi's Island is not a difficult game to beat. I've done it with my feet (no, seriously). To clear with a perfect file, though, is an entirely different matter. You can strive for 100s on all 60 levels, which is hard enough on certain levels (e.g., Secret 5), or you can go for a truly perfect file and pass the game without dying (well, if you miss, you can reset and try again, but 100 on levels like Extra 5 without a Middle Ring is VERY difficult). I know Fifth's done it; I haven't yet.
Mario Party? My worry about this game is that, even if you've just RENTED a Mario Party game, it feels like you've played the game before. Even if you haven't. I haven't played MPA, though, so you never know.
That said, assuming you can only get one game, I'd go with SMA3. Yoshi's Island is really unlike any game ever made (Even the past Mario platformers), and you'll enjoy it, I'm certain. If Mario gets too annoying, you CAN turn off the sound (although there are audio cues that you may need for certain levels... There's a part in 5-4 where you ride a platform ghost that sticks out in my mind).