I can't help but think if you are going to subject yourself to a rule like 3 watches only, then the three watches better cover every occasion. Fortunately I have a lot more spots in my watchbox than 3 so I don't have to put such a restrictive rule on myself.
I noticed that a lot of the responses are like Rolex Sub, Rolex GMT & Rolex Daytona. This makes no sense to me. Why restrict yourself to 3 watches that serve the same function? In my mind everyone needs a minimum of two watches. One everyday watch and one dress, minimum. In my mind a Rolex on a bracelet is not a dress watch. I know everyone thinks a nice sub goes great with a suit, but to me that is pretty tacky and not for me.
#1 Most of the time I am pretty casual and I am a big fan of Divers so I have to go with at least 1 Diver. Personally I am not that big a fan of anything Rolex mostly because its just not the image I want. I'm a bit more "under the radar" so I'm going with a 2018 Omega smp, black dial.
#2) Every now and then I go to a wedding or something else that requires a suit and for me that means at least 1 dress watch that is a basic 3 hander on leather. Like I said, I don't suit up all that often so I am going with a white dial, ss case that I can swap straps from black to brown & make this one watch work for just about any suit I can wear. For this I am going with an Omega DeVille Prestige on leather.
#3) This one I could go a few ways on. I think you could make the argument that you need a watch for working on the car and any other rough activities that you don't want to damage your nice Diver. Something like a g shock would fit. There are probably a few other ways you could go with this third one, but since I am a big fan of Divers I am going to go with a more affordable Diver that I am not afraid to wear banging around the garage. My choice is a Seiko 62 MAS sbdc051. All the SS is hardened with Seiko's diashield process & it has a Sapphire crystal so this one can really take a beating without looking beat up.
I'll come back later and add pics