Party Play is for players who play Animal Crossing on the same Switch. You’ll need your own controllers, but you can play split-screen with each other. (It’s a good option for family members. ) Local Multiplayer is for players who all have Animal Crossing on their own individual Switch. You’ll need to be in the same room to play together, but you don’t need to share controllers or screens.
The subscription will automatically renew itself by default. If you don’t want to renew your subscription, you’ll need to cancel automatic renewal through your Nintendo eShop account. If you use your Switch regularly and would play online often, it’s cheapest to get the yearlong membership. If you don’t play for weeks or months at a time, though, the one- or three-month membership (without automatic renewal) might make more sense. You can also get a weeklong free trial, but you can only use it once.