Just to clarify, the One Piece anime is good, but the manga is even better. The drop in quality of the anime is really noticeable after the time skip. This is due to the anime trying to fit the one chapter one episode ratio. It's very difficult trying to extend one chapter in a manga into 15-20 min episode.
Remember when everyone complained about how long it took for DBZ characters to charge up their attack? This was done because the manga was still ongoing and the anime was trying not to catch up. Same concept with One Piece, but instead of charging attacks, it became long drawn out facial expressions for everyone including fodder #1, fodder #2, fodder #3,4,and 5, and the kitchen sink. This is really noticeable after the time skip.
With that said, the earlier OP episodes followed a 2 chapter 1 episode ratio so things aren't as dragged out. Of course the quality of the animation wasn't as good(late 90's early 00's animation). It gets much better after the first 50 episodes.
If it were me, I'd read the first 100 chapters, pick up on episode pick up on episode 62(so you can skip the filler episodes 54-61) and then watch until the time skip. Pick the manga back up afterwards. then watch the 2 of the specials (Episode of Luffy and Episode of Nami) to watch the first part you read in manga in much better quality.
With that said, also watch Full Metal Alchemist Brotherhood, Code Geass, Magi, Yu Yu hakusho, Samurai Champloo, FLCL, and Fairy Tail.
if you feel like reading at one point, read Tower of God. It has no anime because it is a Manwa(Korean Manga), but all the drawings are colored and has world building and character development on par with One Piece. It is my 2nd favorite series.