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.