Normally this is another way to say "I chose the watch". I had to make a decision between buying my friend a watch and a diamond ring...but I didn't have that much money, so I went for the watch :)

Go for it! That's a common phrase of encouragement. "Should I buy that watch on ebay?" "Go for it!" "OK" (five minutes later:) "Ok, I went for the watch. I'm not so sure about the matching umbrella though."

Kayleigh's answer is most probably correct (she has good answers). There is one other possible meaning for this sentence. If I had left a watch with a repair shop and went out to get it when the shop told me that it was repaired. If somebody asks me why I went out, I might answer "I went for the watch." The meaning would be "I went to get the watch."