Your bank comes with you.
Your stabled creatures come with you.
Everything you carry or wear comes with you.
The animal you are riding comes with you.
All animals that are actively following you that aren't in a stable come as well, but it's risky. If the animal decides to stop following (or if you tell it to stay), it can get accidentally left behind.
People moving large amounts of items typically either ride a Giant Beetle and have two Pack animals (horse or llama) following them, for 375 items, or are on foot with five pack animals following for 625 items, in addition to the stuff on them and in their bank.
Again, using pack animals you aren't riding is common, but it's also risky. Put your least valuable items on them, just in case they don't make it, and you can't get help to regain them and their contents.