As someone who regularly plays every Mario Party in the series, this game is definitely one of my top 3 picks. No microphone is required to play this game. Simply go to the in-game options menu and set microphone usage to your controller if you want access to microphone modes/minigames. (Mario Party 6 has this same feature and option.)
If you have a Gamecube or an RVL-001 model Wii capable of playing Gamecube games, I'd recommend getting it. This specific Mario Party might work better for older children (and of course adults) than really young ones.
Techie info on multiplayer gameplay:
-The game supports up to 8 players, but since four controllers can only be used, two people must share each controller. This can be avoided with 4 or less people playing.
-It is possible to control and play as two characters simultaneously if you want. This is not recommended if you are new to the game, but it's a possibility that is surprisingly easier than it sounds.
-The game has general party modes for 1v1v1v1, 2v2 (where players can choose to double up on a controller), 2v2v2v2 (where players can choose to double up on a controller), and an alternative 1v1 gameplay-style mode (called Solo Cruise). I believe you have to unlock the last one for multiplayer purposes in game, if I remember correctly.
-If you do happen to own a physical microphone, everyone shares the same mic. The mic content is only available in situations where there are 4 players or less. Of course, you are not forced to use the mic, and mic content can be played on Gamecube controllers anyway.
-Like in every other console Mario Party before this one, it is possible to add/remove/switch players in a game with another. This specific game requires at least one human playing at all times, however.