I don't know if there is any one best ship for singles and most cruise lines will mount a marketing campaign to attract certain demographics,( i.e. Disney markets to families with children so logic would reason that is not a good cruise line for singles but my girlfriend just returned from the Magic and noted there were several single family parents with kids) so it really depend on a number of factors. You might check the chat room on cruisemates for singles to identify some prospect. I would suspect the best cruise line or ship is the one that year after year caterers to large singles groups or focuses on themes that would attract singles so you might locate a good travel agent that can do some leg work for you.
But you know, sometimes you never know..way back in the early 80's Carnival had a deal where you could stand by on the day of departure and pay $395 p/p and if there was a no show you could get a cabin (can't do those things today due to 9/11 and the introduction of the internet as an active booking tool). One time I went with my best friend who happen's to be a female and we never had a relationship, but were great cruising buddies and wouldn't you know it, there was a group of 400 single secretaries from NYC on the ship and none of them would give me the time of day because they thought my friend and I were a couple (my friend just laughed and laughed)..the second time I did the stand by thing on Carnival, I went with a male buddy of mine because we thought we would meet lots of single women and almost 2/3 of the ship consisted of a group of gay men (this is back before the travel industry catered to them) and do you not know that my running buddy and I had the best time (fyi, they knew we were not part of the group). To be safe, I would find a bunch of my single friends and convince them to go with you on your cruise..good luck