If you want to follow the story of One Piece, your only choice is either to watch the anime or to read the manga (you will complete it much faster since you can read a chapter in few minutes). Also a big bonus point for the manga is that there is no filler.
Regarding the movies, most of them are not-canon which means they don't fit in the story of One Piece. You can view them as a spin-off, which takes the existing characters and world setup but tells a totally different story that is in no way connected to the anime/manga.
So, in short, the only way to follow One Piece is either to read the manga or watch the anime.