Pick the cruise line first, then the ship: ships on the same line can feel very different, so the ship matters almost as much as the line. Look at three things: its size (which shapes the energy and how steady it feels), its age (newer ships have the newest features), and where it sails from in your dates.
Size
Bigger ships carry more people and more to do: water parks, multiple pools, big theaters. They also tend to feel steadier at sea. Smaller ships feel calmer and less crowded, and can visit smaller ports, but they move more in rough water.
What I noticed: I've sailed two Royal Caribbean ships, Oasis of the Seas and Enchantment of the Seas, and they felt very different. Oasis was much more energetic, with a younger crowd and far more to do. It carried significantly more passengers, but its layout spreads people out across separate neighborhoods, so it felt less crowded than it should have. Enchantment was calmer, with fewer activities, and I could feel the ship's motion much more.
Age
Newer ships, and older ships that have had a major refurbishment, usually have the line's latest restaurants, bars and activities. An older ship from the same line can feel quieter and more traditional, which some people prefer.
Space per guest
Two ships of the same size can feel very different if one carries many more passengers. More space per guest means shorter lines and calmer pool decks.
Sister ships
Many lines build ships in "classes" of near-identical sisters. If two sister ships sail from your port, they'll feel very similar on board, so choose between them by itinerary, dates and price.