Why the album cover seems blurry

Hello everybody!
First of all: yes, the search function was used extensively !!
My extensive iTunes collection (13,000 songs) is nicely organized and categorized, but what doesn't work that way is the cover display in Flow / Ipod mode on my Iphone 4. Most of the covers are blurry and fuzzy, even though I was a long time ago I've started adding the covers of each album using drag & drop from Google image search. The covers that iTunes loads themselves seem OK, but often iTunes doesn't find my albums to be too exotic.
When adding covers manually, I always paid attention to the highest possible resolution (at least 1200x1200 pixels). My naive assumption was: the higher the resolution, the sharper the image on my iPhone. After a long research this seems to be wrong, apparently 300x300 are sufficient; It was often said that too high a resolution would make the pictures blurred (?). So I now have a colorful hodgepodge of different resolutions (to be honest, I don't know how the covers were saved, whether as an id3 tag or something). Hence my question (s): is there a reasonable tool that standardizes my covers, optimizes the display on my iphone and finds as many covers as possible (I found mp3Tag while searching, is that good?). Which resolution is optimal when adding new albums? 13000 titles want to be processed first, so I wanted to ask the forum for advice first, maybe others have this problem too. Thanks in advance!"!