You don't have to get them extracted unless they are causing pain. If they get compacted, you will then need to get them removed. They are one of the various leftovers from our evolution..from when we had larger jaws which aiding in the chewing of plants. Not everybody develops these vestigial third molars. Some develop 4, some only 2, etc.. They typically develop between the ages of 16 and 24.
Personally, I developed two. One was partially compacted. The other was causing no issues. I had them both removed for preventative purposes. I had local anesthesia but you can also get general anesthesia. The choice would be up to you. General might be the way to go if you don't want to hear the extraction process....which involves cracking the molar and pulling out the pieces. The sound of the tooth cracking and being split as well as the associated "squishy" sounds of the removal can be off putting to some people.
Pain is all dependant on the person and is difficult to classify. Typically, you will just feel a long, dull pain in your mouth. But you will normally be prescribed pain medication if required. For me, there was pain the first day but it was extremely nominal on all subsequent days.