Leads can be crafted in pairs for 5 string per craft. It takes 5 string to craft 2 leads, 10 for 4, 15 for 6, and 20 for 8. Wandering Traders will always spawn with 2 leads attached to trader llamas. They have a very low chance to spawn every 20 minutes. You can also get leads from Ancient City chests (16.5%) and Woodland Mansion chests (32.9%).

Small flying mobs like bees, allays and parrots are easy to lead over long distances, and mounts like camel, horse, donkey, and llama are easy to lead over uneven terrain. If you're boating with leashed mobs, make sure to break the boat as soon as you get out, as the lead will detach if a mob gets in.

I go over the mobs you can leash in this bad YouTube video, but here they are listed out. The green mobs are the easiest to find, yellow mobs are easy to find but biome dependent, orange are harder to find and red are quite niche. Baby mobs don't count as separate mobs, and boats / chest boats don't count towards the goal at all. See below on keeping mobs alive.

[1]  This mob can be kept in your inventory until you want to spawn it in (either by constructing or unbucketing it).

One of the main concerns when hauling 8 mobs around is that they stay alive, and especially that they don't kill each other. 

[2]  Due to this mob retaliating, you can make it aggro onto you instead by punching it to override its hunting AI. Poar bears cannot hit you if you pillar up 2 blocks. 

Goats can ram any mob that is stationary, dealing 1 damage but 9 blocks of knockack, but no mobs except Hoglins will retaliate. 

Iron Golems will NOT attack camel husks, zombie horses, or zombie nautiluses. 

Snow Golems will take damage in water, rain and hot biomes, though similar to Axolotls, you don't need to spawn them until the end. 

Wolves should ideally be tamed (or punched, see above), and Cats too if you are hoping to leash a rabbit. If this is not feasible, however, you can trap some of your mobs in the ground and acquire them piecemeal, as long as you remember which mobs attack which.

Hostile Mobs can also attack your mobs. 

• Most monsters will attack Iron Golems; 

• Drowned, Guardians and Elder Guardians will attack Axolotls (but bucket); 

• Guardians and Elder Guardians will attack Squids and Glow Squids.