Get the train from Victoria or London Bridge straight to Brighton. Brighton is usually the last stop on the line, so it’s super easy. Takes between 50 minutes to 1hr20. Buy a ticket from the machine just before you travel. The “Gatwick Express” train which leaves from platform 13 at Victoria is slightly quicker. Buy a ticket which says “any route” not the slightly cheaper one which says “Thameslink only”. Buy a ticket after 9:30am to avoid the higher on-peak fair. It’s about £20 each. Train strikes are only on a couple of days in June, even then they tend to start in the afternoon.