If you don’t have experience a Rolex isn’t a good watch to start on.
Stainless steel isn’t easy to work and polish, and trying to get a good finish on a flat surface like a centre link is quite a challenge.
The way I’d tackle this depends on how heavily marked and scratched the bracelet is. It may be possible to refresh the original brushed finish but if it's heavily scratched the damage needs removing first. I do this by hand, using a small hardwood block and various grades of wet and dry paper. For the final brushed finish a Garryflex blue block, coarse Scotchbrite pads, or 600 grit wet and dry all give the right grade of finish. I also use a wheel made from scotchbrite- type material on slow speed for final finish to get the
graining straight.
For the polished parts, use 1200 grit wet and dry wrapped around the hardwood block to get the scratches out. Work through the grades ( 1500, 3000, 5000, 7000) before polishing with a buff stick and metal polish. Final finish is done on a polishing wheel.
At each stage I use the brown plastic masking tape that Cousins sell, its heat- resistant so it’s OK with the polishing wheel. I have a piece of hard rubber pipe acquired from work many years ago that I fasten the bracelet around, I used it as a stress ball in the past and it now serves nicely as a support/ former for this work. Double- sided adhesive tape is used to secure the bracelet pieces.
I would expect to spend around 3-4 hrs doing it my way, it’s tedious work and I’m no longer interested in taking these jobs on.
Trying to polish the centre links with cotton wool buds is like boring through a mountain with a carrot, metal polish on a buff stick is the way to go, but only after you’ve taken the scratches out with wet and dry.