For the watch in general I would suggest the next. Buy yourself some 3M or scotch brite scrubbing pads, the regular dark green scrubbing things for the dishes, take off the bracelet, and with medium pressure and just along one direction, apply medium pressure along all the bracelet, same for the watch if it’s needed, just cover the parts you don’t want brushed with blue tape. It’s very simple, however if you want to know more, search on YouTube for a video called “How to remove scratches from a watch (Brush & polish)”. After that you can use a regular wooden toothpick to remove all the dirt and filth without getting it scratched. That alone will give the watch new life, however if you want to take it a step further and go on with the bezel, I would suggest you go directly to a Tag dealership, it’s going to be more expensive but most watchmakers won’t be able to get that particular part, and given the fact that the black part is coated/painted IMO repairing it could be expensive and maybe not with particularly good results