There is Or There are?

Here are some other examples of there is/there are use.

• There’s a lot of reasons to be optimistic. (incorrect)
• There are a lot of reasons…. (correct)

• There’s two sides to every story. (incorrect)
• There are two sides….(correct)

• There’s several storms arriving in the West. (incorrect)
• There are several storms arriving in the West. (correct)

• There’s not options out there that they like at the moment. (I actually heard this one on ESPN.) (incorrect)
• There aren’t options…. (correct)