Repeated words? What is the difference between 見ましょう and 見てみましょう?

Where does　たくさん go in a sentence? If I wanted to say "There are a lot of flies in the room," is it: 部屋にたくさんハエがいる。 or 部屋にハエがたくさんいる。 or is a completely better way to put it?