What is the best way to store large lists of user statistics?
As others have mentioned, I'd look to normalize the data in your UserStatistics table. You could do something stupid simple as a generic Likes table and a Follows table (don't take my poor names, I'm sure you can come up with better ones :).
The Likes table would have its own primary key, and a foreign key field referencing user_id, and it could have a column called like_id and a column called like_type. The like_id would store one row per ID from the user_song_likes, user_album_likes, and user_artist_likes columns of your previous schema, and the like_type would represent if it's of type song, album, or artist.
You could then implement the same idea for your Follows table (e.g. store one row per ID of each follower and following in a generic follow_id column with a follow_type column to determine which is which). Using a more normalized schema (even though this one is generic to keep things simple) is a more relational form of storing your data and will be more efficient for querying.