I often get confused when trying to use who vs that.

Some examples that often confuse me:

THAT

The person that went to the store.

The people that went shopping.

The persons that went shopping.

The group that went shopping.

WHO

The person who went to the store.

The people who go shopping.

Please explain when to use either for plural subjects and singular subjects. Animate and inanimate objects as well.

Thanks!