I just wipe the exterior with a paper towel to avoid water spots. The frypan, and the saute illustrate what it is like if you don't wipe after washing. I don't polish. Took me awhile to figure it out. The hammered pieces, which I do wipe, end up with a patina but not mottled/spotted like the aforementioned.
The tin gets dark but that is alright. A bit of a learning curve to use silicone utensils to avoid damaging the soft tin, but the advantages, for those who like tin/copper are there. YMMV ........ :)