Most swimmers wear a swimsuit specifically designed for swimming laps. They typically have a sleek design with flat seams to prevent chafing. You'll also need a suit that can stand up to water wear and tear. For instance, Nike HydraStrong fabric provides long-lasting durability you can depend on swim after swim.
You'll also want to invest in a good pair of low-profile, flexible goggles and a silicone swimming cap to reduce drag. For outdoor swimming, some athletes prefer a wetsuit for cold-water conditions. You may also want to invest in training tools like a pull buoy or hand paddles, if they're within budget.