@Inhaki thanks for the question
The initial change from new to used is the biggest. The marks on the surface will naturally fade with use and blend into each other and come and go. For reference here is an image of my personal Type 15. This razor is 1.5+ years old now (this was a prototype) and the visible marks are not what they were 3 months ago even and overall the color is very even and stable now.
I have found a great difference between cleaners and soaps, some brighten the brass, some darken it, others remove water marks, some don't. This is why it is hard to recommend one particular product. A very mild polish will certainly return the brightness to the surface, as well as offering a protective barrier for a while. But I wouldn't recommend a heavy polish, or using lots of pressure. Vinegar is a good place to start perhaps, just mix some with some water 50/50 and place the parts in for a few mins, or you could try some neat vinegar on a cloth and then rinse with water and dry to help reduce/remove the water and soap marks. You can try some light bees wax on the surface to keep it more stable if you like too, it seems quite effective.
It will settle down with use and become much more even, but it will always have some signs of use from now, but this is unique and with more use will start to really amount to something personal. Its perhaps a little cliche, and very much down to your personal choice but I like to think the brass Type 15 will become beautiful, functional, heirloom one day.
Hope that helps?
Andrew.