We don't need alphabet soup or a governing body to enjoy clay sports, we just do it.
Some semiautomatic shotguns are less reliable than pump shotguns. The inverse is also true. First hand experience with the individual example you intend to use with the ammo you intend to use is really the only definitive way to know if a shotgun is "reliable". Many people will encourage you to "research" which brands are reliable. This of course involves going on the internet where misinformation and second hand lies are rampant. Also people who bother to post about the reliability of a certain model are much more likely to be the vocal minority of those who have experienced problems. Anecdotal evidence from friends and family is equally worthless unless they are trustworthy and are purchasing their shotgun from them. Buying a gun with a warranty and then putting it through it's paces is the only way to ensure you have a reliable example.
You'll have to handle them and see what's comfortable and what you shoot well with. Your height is really irrelevant, it's the length of your arms and stance/grip preference that ultimately decide what works best for you. It's something only you can decide for yourself. A veteran shooter can still be of great help, but realize that you are the ultimate authority on what works for you. Try everything.
