I wear my watches for golfing, swimming, wake boarding, tennis and everything in between.The manufacturers will recommend that we stay away from activities that has impact and vibration. But I have done all of the above and I know many others who also do the same and more. Some even work on construction sites with their Rolex. Nothing to worry about. You buy a watch to wear, and not to baby. Please don't get me wrong and I do not mean to offend. There will be knocks, there will be accidents and stuff that will scratch your watch, ding your watch and put marks on your watch. If you don't want that to happen, then please by all means buy your timepiece and put it in a glass case to admire.
Accuracy for that matter varies from one mechanical watch to another. Unless you have yours constantly regulated. Or you can self regulate by putting them in different positions while you sleep at night, i.e. face up, face down, crown up and crown down. But no one mechanical watch will be absolute in accuracy. Otherwise you can go get a quartz. I will adjust the time of my watches on the 1st of every month. And the website that I use is time.is.
Good luck and don't bother too much about your watches. They are tougher than you think.