Cruising is the best way to start travelling solo, because everything is arranged for you -- you don't need to plan where to go to dinner, or worry about walking into a bar alone; there's entertainment options all nearby if you want them, but safe and quiet places to go if you don't. You will see the same people around the ship so often, they won't be strangers for long, and that will make it easier to strike up conversations with them, and you will all have some shared experiences (which are great for starting conversations).
I think a 10 day trip is a good one to start solo cruising -- cruises of 7 days or less tend to have more of a party vibe, and cruisers are more likely to want to hang with the people they came with. In a longer cruise, more cruisers are (in my experience) more laid-back, willing to talk with other travellers, and less focused on being busy all the time.