You need five things to go surfing: a board, something to wear, a leash, wax and sun protection. Everything else is optional. This checklist puts them in the order you should buy them and links to the full guide for each.
TL;DR: Rent for your first week. Then buy in this order: wetsuit, soft-top board, leash, wax and comb, sunscreen. Add a board bag and booties when you start travelling.


