For Damask and Nanny, do think again. NOT all cruises are alike, cruise lines and ships are very different!!! But they all have loads to do, and your hotel room travels with you!
If you WANT a huge ship, like a floating city, plenty to choose from.
If you'd like a smaller, quieter ship, also lots of those, and as Madeleine says, Fred Olsen are indeed geared to the more mature Brit passenger. Cunard are too, but the passengers of that line that we've met on other ships could generally be classified as Snobby on Steroids, so we've avoided that line (apols to any Cunarders reading that who are perfectly decent agreeable people, but sadly some other passengers don't spread that word!).
Lots of higher-priced 'smart casual' lines, all have fabulous service, usually much smaller ships, Oceania, Regent, Seabourn, Hapag Lloyd and more, and similar service but hopefully not quite so dear on Azamara.
BE VERY WARY - unless you're a party beast?! - of lines like Carnival, and NCL (a Carnival cruise got famous few years ago for taking a block booking from a Hells Angels group, quite a shock for the other thousand or so 'normal' passengers who had their vacation ruined!).
Oh, and if you like a more 'multi-cultured' trip, try MSC somewhere in the Med, they'll likely have local passengers getting on and off at each port. A disadvantage might be that you'll get ship announcements, and in the cabaret, in about 6 languages, English well down the list?! But MSC was the only ship we've met that had opera on the cabaret one night, appreciated by a rapt audience (best not every night though?!).
What else -- the dressing up thing??? Well, IF you like that, lots of ships do formal nights, maybe 3 on a 2-week trip, and some women take a delight in wonderful outfits, and their gents usually look good in a tux. We DID do that once, IsNibs hired evening dress on the ship (Celebrity I think, they're OK too), but we've now got used to swerving that type of thing, by using the evening buffet, or one of the speciality restaurants most ships have (& NO, Sago, we've never caught any of the germs you're fascinated with!). We're now keen on the 'smart casual' mantra, saves on luggage space!
For new cruisers who take the plunge, do some research before you go, and TRY to avoid the Ship's Tours, the most complained about aspect of cruising, on all forums, for years. They get many moans for being over-priced, and often poor value. IF you're able-bodied, you can usually do better going on your own to where you want, and not in a crowd. Disabled folk usually are obliged to use them, but these days via the i'net you can sometimes liaise with local firms directly? Bear in mind that in Greece (& a few other countries) the signs on buses will be unintelligible, so public transport is tricky?!
Some of the upper-crust lines INCLUDE some tours (possibly Saga too?) but you're paying a higher price up front anyway. 'Tips' (often called Gratuities) MAY be included in the price, but may not, so do some research on that too, as to new passengers the concept may be a surprise?
IF IN DOUBT, seek advice from an expert cruise booker like IGLU, or one of the forums eg Cruise.co.uk. Somebody somewhere has asked your question, or done your trip!