I love cruising, so I would say do it. You'll see so much, meet lovely people and learn lots. It's a very comfortable way to travel.
They have excellent medical facilities, although they are expensive, so you need good insurance. I've even experienced requests for blood donors far from land, so they do their best for the severest problems.
The longest I have done is 11 weeks around South America, including up the Amazon. I didn't want to get off.
As PP say, you need to do your research and a week or two cruise would be good to make sure you don't hate it. A long trip has a very different feel to a holiday, however. It attracts people who are really interested in the travelling, rather than a break and of course people who can take the time off, so tend to be older. But as PP say, insurance can be an issue so it's mostly young older people who can afford that and feel up to travelling for a long time. There are plenty of companies offering cover for long cruises and many include pre-existing conditions.
It would be easiest to go from Southampton so you can take as much luggage as you like. P&O and Cunard run World Cruises of around 100 nights, usually leaving early January. P&O would be cheaper, their drinks are city pub prices, gratuities are included and their tours tend to be cheaper, but Cunard don't usually charge daily gratuities on World cruises. With both you can take a little wine and any soft drinks you want on board to drink in your cabin. You can also buy soft drinks ashore as you go, but water, tea and coffee are included and there is a kettle and cups etc in your cabin, so you could take hot chocolate. The launderettes are free, Cunard provide washing sheets, P&O don't. Neither of these lines 'nickel and dime' you, you can spend 100 days on board and quite easily buy nothing extra. There are things like extra restaurants or drinks on offer, but no pressure. They also offer excellent free talks on board, specially during the longer cruises and all sorts of free classes. P&O tend to only use their two adult only, smaller ships, Aurora and Arcadia for World cruises. Cunard encourages dressing up about twice a week, but a couple of posh frocks or similar should do and it is quite fun to get involved.
There are lots of other cruise lines, but watch for things like gratuities, no kettle (do you mind running through the ship for an early-morning or late-night cuppa?), laundry service only, etc. A proper walk-around deck fairly low down is a real asset on a long cruise, for exercise, social life and the joy of walking about and gazing out to sea. Also experiencing some interesting weather!
We only use cruise excursions in exceptional circumstances. We either explore on foot or using public transport, pick up a tour at the port gate (join some other people and haggle for price), or use a company like Viator or Get Your Guide, depending on the port. Often you can team up with people you meet on board and book a trip together. Every operator I've used is extremely keen to make sure you get back on board in time, so I wouldn't pay for ship's tours just to be sure of getting back. The people who get left behind are the ones who go off on their own and forget the time, or get very drunk.
I find the Iglu cruises website is very user-friendly to see what's available, although I wouldn't necessarily book through them, I prefer to book direct. Websites like Cruise Critic, Cruise Mummy, Facebook and You tube carry loads and loads (too much) information and opinions.