It depends on which game it is and who is available. I don't necessarily have a dedicated "main" like in other games, instead having certain ones that I swap between.
I played the original Mario Party as a child when it was new, but I haven't played it since then, as I only rented it from the video store and never actually got a copy for myself. However, I'd probably opt for Peach if I were to play it again. Donkey Kong also has some appeal since he eventually leaves the playable roster to become an NPC.
Mario Party 2 is also a Peach (or DK) game since it has the same playable characters.
Mario Party 3 introduced Waluigi and Daisy to the Party games, and I like them, so they (or Peach or DK) are most likely.
Same applies for Mario Party 4.
Mario Party 5 added Boo, so obviously going for Boo, but I'll alternate with Daisy, Waluigi, and Peach like before if I just want to switch it up for whatever reason.
I have Mario Party 6 and 7 but don't think I played them much because of the microphone. A shame, since they added Dry Bones in 7.
Never played 8, 9, or 10, nor any of the handheld installments for the GBA, DS, or 3DS. Is 8 any good? I just kind of didn't pay attention to it at the time, I guess, probably because of the disappointment with 6 and 7. For 9 and 10, I saw the car mechanic and just wasn't interested. As for the handheld installments, I didn't know about the GBA and DS titles when they were out, finding out about them later. I knew about the 3DS ones but just never bothered.
Only played Super Mario Party at a friend's once, but if I were to play it again, probably Boo, Dry Bones, or Rosalina.
Finally, in Mario Party Superstars, I usually use Rosalina (or Daisy if someone else picked Rosalina) or Waluigi.