Simple: We will go to the park then lunch.
Simple sentences follow a simple structure with Subject then verb. There is only one subject and one verb phrase to create a complete idea.
Compound: Let's go to the park first, and then we'll go to lunch.
A compound sentence combines two complete ideas into one sentence using either a semicolon or a comma with a conjunction. In this compound sentence the comma and conjunction "and" join the two complete ideas together.
Complex: After we go to the park, let's go to lunch.
This is a complex sentence. A complex sentence contains a dependent clause, "After we go to the park", and and independent clause, "let's go to lunch".
Compound complex: Let's go to the park first, and then we'll go to lunch since we'll be hungry.
A compound complex sentence contains both a compound sentence and a dependent clause. In this sentence the dependent clause is "since we'll be hungry". It was added to the compound sentence answer.