Give your vet or if you don't have one, contact a vet that does vaccines and ask about vaccines you need for your horse to attend shows as it all depends on your area or even the area you are traveling to.
I would have your vet give your horse the basic vaccines whether you plan to show or not. 6-way + rabies is what mine get. Some shows may require a proof of negative coggins, so definitely get that one done as well!
It depends on where you're showing. Look at the biosecurity risks for your area.
A good place to start is vaccination for flu, rhino, and tetanus (you never know when your horse will find a rusty nail).
Some places have high incidinces of west Nile, rabies, or strangles. But you'll need to see what has been reported in your area and where you'll be showing.