Question

What type of logical fallacy does this give the lord of the rings is my favorite trilogy because its so good

Answer 1

This can fit into the category of Hasty Generalization, this is, that you generalize  with a lack of evidence or better,reasons as of to state that the trilogy of the Lord of The Rings isgood. It is good because it is good, if the first part is good, then all the trilogy is good.

Another option might be a fallacy called ad populum which takes place whenever you appeal to the public knowledge of something to prove it is true. In this case forexample, you could say: the reviews are giving this movie 5 stars, so this movie is good, because people like it.