There's a lot more to it than height. It's worth getting fitted at a shop. Road cycling is all about fit and positioning. I'm six feet tall and ride a 58 cm but others might ride a 56 or 54.
Most people that are your height ride a 58cm but it does depend on the bike and the rider (leg to torso ratio etc) I'm 5'11 and I ride a 58cm or large (19-19.5inch) on mountain and road on almost every bike I've ever ridden or owned. I've had two Giant TCR road bikes, one Trek Madone and one Bianchi Pesta all 58cm and I've ridden a Trek Domane same size. I've also had a Trek Superfly and a Giant XTC and ridden a Trek Remedy that were both larges. I also had a large (58cm) Giant Trinity Time Trial bike and that is the only bike I've ever ridden that I probably should have bought the 56cm.
If you find something used you can probably get a 56 to fit you but you are going to need a longer stem which spoils stiffness and makes the bike look funky, plus smaller bikes are less stable and road bikes a less stable than mountain bikes so you'll probably end up going with the 58. Whether or not you buy new or used though you are going to definitely want to go to a shop and get fitted. With road bikes the difference between a heavenly bike and a total crap fest can be a couple of centimeters. Definitely worth your time and possibly money to do that. As far as different bikes go? They are all pretty fantastic, if you just want something cheap, durable, and smooth go with steal or alluminum (alloy is more common and lighter but not as smooth). If you want something super fast and light but aren't necessarily looking to race get and endurance road bike like a Spec Roubaix or a Trek Domane. If you want the absolute fastest most aggresive bike out there, that's a whole other can of worms.