Safe driving begins with you. If you give yourself enough time to get to your destination, stay cool, collected, and focused on the road, then you don't have much to worry about.
Avoid getting ticketed by obeying the speed limit and road signs. Driving safe will also help improve your insurance rate. And you will avoid accidents. All great reasons to drive responsibly. You should also make sure that you keep an emergency roadside kit in your car and do your pre-checks, especially before a long trip. Even before you get behind the wheel, you should check for leaks, top up your fluids, and check your tires. You should have good tread and your tires should be properly inflated.
You may not be able to avoid accidents and breakdowns completely, but you can be prepared. If you are prepared, then you will be better able to handle almost any situation.