First of all, are you left handed or right handed? Wearing your watch on your non-dominant hand tends to have more practical advantages. Sure, you can wear your wristwatch on your dominant hand, but that can lead to avoidable issues down the road.
If you're a right handed person and are more active with your right hand, then placing your watch on your left wrist reduces the likelihood of damaging your watch. Direct contact with harsh household cleaners and hard surfaces by accident can damage your wristwatch's surface. We're not talking about stains or scratches that you can buff out with a cloth with water. Your watch is also more likely to get in the way when you're moving your dominant hand around. Scratches and cracks are inevitable if you're not careful. Continuous damage over time to a metal band can ruin the integrity of its band latches over time. The opposite is the case if you're a left handed person. Placing your watch on your right hand can reduce the likelihood of damaging your wristwatch.
It's easier to see and set the time when your watch is on your non-dominant hand. Have you ever tried to write with your non-dominant hand? It's really difficult if you don't have a lot of practice. It's not precisely the same as adjusting a knob, but people find that it takes slightly longer if they're using their non-dominant hand to adjust the time.
If you're right handed and married, wearing both your watch and your wedding band on your left hand could be preferred, especially if both accessories complement each other well. Now if your wedding ring and watch are both heavy pieces, it may be wise to spread out the weight between both hands so it doesn't feel like one hand is weighing down the other.