I'm taking my first cruise solo on July 7th on the Imagination sailing out of Miami, I'm 35, and had some concerns myself. Carnival cruise line said that they have get togethers for singles to meet, you simply need to read the daily activity brochure to see where and when what's taking place. One way to meet others that are sailing on their own.
They do have a lot of things to do while on the ship: gym, spa, casino, clubs, ping-pong, shows, dance lessons, etc. All else fails, they have 3 or 4 channels that play movies all day long....
Also, if booking a cruise for yourself, you'll pay extra for your ticket. For myself it was the cost of my ticket (for example, say ticket is $400 double occupancy), since it's only my in the room, I than had to pay 50% of the other ticket (add $200), for a total price of $600 that I had to pay.
When booking, ask it they have any specials or cheap rooms available - skip the balcony room. If you're flexable on your schedule, you may be able to find something better priced.
Hope this info is of some help,