Make sure your shoes fit your feet and your style of running. Keeps the wind out of your eyes on the bike, and makes the run more comfortable when you don't have to squint in the sun. Whether for comfort or modesty, many people prefer having bike shorts or running shorts for the segments after the swim. If you're more concerned about blisters, take some time to put on socks for the bike and run. The most important thing about the gear you use for a triathlon is comfort.
Individual preferences vary.
Some people feel comfortable doing an entire race in a swimsuit. Others who aren't concerned with transition times will change clothes for the bike and run.