Good point, but what do you consider classic?

sorry ... I deleted my comment. it sounded a bit snarky when I reread it, and I didn't mean it to.

If your "modern" tastes lean towards Mid-Century Modern, then I would go with Chrome. Many of the iconic MCM pieces have chrome (think eames loungers and platner dining tables).

If you prefer a more zen-like nature inspired modern, then go with brushed/satin.

Unfortunately, anything you do now will eventually be "dated" because styles and trends are always changing and evolving. I would pick a finish that you like, because you'll have to live with it. I would suggest keeping it simple, and even through the finish name and sheen will change it will still look good. Brushed has been around for a long time and will probably have the best chance of staying more "current."

Chrome

Brushed is what I see most often in recent makeovers. And I think that brushed may not annoy people who prefer the shiny, as much as shiny would annoy people who prefer brushed, because it does have a calmer feeling to it. I know that everything can look dated at some point, but that's more true of some things than others. (Of course, if it were obvious at the time, nobody would install all that stuff that gets ripped out 5 years later.) I personally feel that the brushed is more sophisticated, intrinsically, so it's a safer choice.

IMO Chrome, other finishes have come and gone, but chrome keeps coming back. I think that chrome is like a neutral. One of the high end builders in Florida is using chrome for their fixtures in their new model home. But it really comes down to what you like.