Hi OceanSkies (good name),
I have sailed 11 times, all solo, the past 7 years. Here are my thoughts:
You are right, cruising is the most bang for the buck. It's so easy to unpack once and get taken to new places everyday; plus all the activities onboard ...nightly shows, casinos, spas, buffets, etc.
I have found, and most people agree, that people on cruises are usually friendly and eager to meet and chat with others ...just don't be shy. A good way is to comment on the view, or whatever, to people leaning on the railing next to you (you choose who they are first,
), and hopefully start a conversation. Or ask someone of interest to take your picture. If you can break the ice, you'll make friends.
The staff treats everyone the same, they don't know if you are alone or not, except your cabin steward and your table servers. Make friends with your cabin steward early, ask him/her for their "best animal towel" and slip him/her a gold dollar or two or three (available at banks), it's fun, makes your steward think you are a good passenger, and well worth the few dollars to create a good connection ...it will pay off. Do the same with your main server at dinner, ask for something you like, such as decaf coffee with cream and sugar at the end of dinner, or sweetened ice tea as soon as you sit down, and slip him/her a gold dollar or two also ...you'll get what you asked for every night, and good service too.
There are (almost) always two specific formats for meeting other passengers, early in the sailing. One, a "singles" meet and greet usually at a bar; and two, a "Friends of Dorothy" meet and greet, which is especially for gays/lesbians/bi's, also at a bar. Both will be advertised in the ship schedule, but ask at guest relations if you need to. Don't miss the Friends of Dorothy meeting; but go to both ...just because you are gay don't miss the singles meeting as a way to meet some people.
Re which lines, I think Carnival is your best bet if you are young (or older), and adventurous ...Carnival promotes a party atmosphere. Carnival also puts singles together at the assigned dining at night in the main dining room ...ask for an 8-top table when you make your reservation, and presto, 8 singles together each evening to share dinner and get acquainted. It's not hard to go from that to attending ship activities together, and even shore excursions (whether any are gay is luck of the draw).
Don't be afraid to ask the maitre'd to change your assigned dining table if the others at the table are not a good match ...people do it all the time (but don't be too quick to judge, and be flexible). The maitre'd has the ages of everybody and whether they are solo or not, so ask about the diners at the table he/she suggests.
Celebrity also puts singles together at the assigned evening dinner in the main dining room. But personally, I don't like Celebrity ...it is much more "solemn" than Carnival, the ships are decorated in "bank lobby" theme (boring), and the ship layouts suck (the worst I've sailed).
Princess has the very best ships I've sailed for design layout (provided it's either Sapphire, Diamond, Glory, Crown, Golden, Star, or the best of all, Ruby and Emerald). They have a great multi-tiered resort like aft, and a great nightclub on the very top of the ship, with views to everywhere; plus a huge glorious viewing area atop the bridge (not present on many ships); and a complete wrap-around promenade deck. Princess is also more "sophisticated" than Carnival, not as much party atmosphere, but still fun and not as boring as Celebrity.
And finally, I agree, nothing beats a private cabin to yourself. Also going solo means you can do whatever you want everyday, without having to coordinate desires with anyone else ...but it can be less social, and if you crave companions, that is, can't entertain yourself alone, then think twice about going alone. It's not certain that you'll meet any others to play with; and if you do, there will certainly still be alone times for you.
Don't miss the ship experience, walk the deck at night under the stars, watch sail-away from the ports (and arrival if you can get up in time!), explore! And don't use your cabin for anything other than sleeping and grooming (unless of course ...you get lucky).
People make their cruises either fun or nightmares, or in-between, depending on their actions and mind-sets, and their reactions to what goes on ...be easy going, flexible, and don't sweat the little things.
Hope this helps!! Have Fun! And let us know what you decide (just add comments to the post thread you started) ...maybe I'll come along! Ha.