If you go from Southampton you have to spend several days at sea getting there and back (which you may like) and can't go very far into the Mediterranean in a week or two.
If you have to come from Ireland it seems to me it would be no more hassle to fly direct to the Med, or wherever you'd like to go, than slog to Southampton. Unless you want to drive.
Watch out for added extras - some lines automatically add daily 'gratuities' which you can have taken off, but you might feel a bit mean, specially if the staff have been lovely to you, which they generally are. You often get offered drinks packages but they may not be worth it unless you drink more than you'd like and generally both adults in a cabin have to buy a package. Shore excursions will be extra. You can book ship's excursions, wander off on your own, book through an independent operator, or there are almost always taxis at ports offering trips when you arrive. If your return to the ship is delayed it will wait for a ship's excursion, but not for independent travellers - you'd have to get yourselves to the next port!
Check out family cabins carefully - it can be an awful squash to have a double bed, a sofa bed and a bunk descending from the ceiling.
Another issue that can arise is if the ship's main language is not English, announcements are made in several different languages and people around you tend to talk over the languages that aren't theirs, making it hard for you to catch the announcement, specially if the PA isn't clear or the speaker has a strong accent. And, conversely, you have to listen to a whole lot of information in several languages before one you understand comes up.
The Cruise Critic website has lots of advice.
For interest a couple of ideas: West Med from Southampton on Enchanted Princess and
West Med from Southampton Royal Caribbean
(I've used iglu cruises with no mishaps, but you might feel more confident to book direct with the cruise line for a little more, which would avoid having to deal with a middleman if Covid problems arise.)