The two button suit is really the design that’s looked at as the classic. Other styles may get popularity over time but it seems to be the standard setup in most cases.
In the 1800s and even up to about the 1950s or so, the 3 button was really the most common. At that point though, the 2 button became more and more popular. The exact reason for the gradual change is debatable. Some say that the more minimal and less formal suit wear just carried down to the buttons. Others say that America suit wearers wanted something that was more slimming, hence the two button look. It wasn’t just an American phenomenon, as the UK saw a similar trend there.
If you’re a taller guy, sometimes the 2 button suit doesn’t quite work. Look at the guys in the NBA. They usually are wearing three, four, and even larger numbered buttoned suits, simply because their body is so long. Two buttons would look out of place. For shorter guys, definitely look into the two as your first choice.
In a three piece suit, the three button look does tend to look better in many styles. It’s a little more formal of a look, although you will see two buttons there as well.
Outside of that, the advantages with a 2 button is that you’ll see more of the shirt and tie. This is good if you like a flashy tie or shirt, or have a well-sculpted chest. For most men it will ultimately become a personal choice. I’ve worn both styles, and like most suits, it ultimately comes down to a good fit.
Just remember when wearing these that the bottom button should be left UNDONE. Yes, you may be tempted especially if you’re not used to suits. But as soon as you sit down, you’ll have a nice tear or button rip to deal with!