The standard methods:
Cards - don't worry about scratches - many serious players sleeve cards these days. It's the most familiar choice. And if the cards are business card sized, they can be hidden in hand or under a hand on the table.
Spinners - not used all that often, however, the mold marks on the back of the spinner may be visible if using the commercial arrows; using a double disk the result can be inferred by watching the pre-choice state and counting the rotations.
I've "read" people's choices in both Dune (double disk) and in El Grande.
dice - also not used all that often, a die with the choices marked as symbols is quite viable; if the choice is reduced to numbers, it's also cheap. It's a bit fiddly, tho.
dreidle - since dreidles are essentially dice, the same issues apply, except that, having only one axis along which choices are made, it's easier to use.
Mat and screen - a mat with the choices marked, and a small marker to be placed upon that mat, with a movable screen - it's got the advantage of being easy to work, and very clear. It also provides a place for faction/side identification and/or cool art, as well as gameflow information.
Marker choice - player takes set of markers in hand, picks correct one
I've used this in SFB for fire declarations. Cumbersome for many, due to half-inch square 1mm thick counters being the mode. Similar issues to cards, but since the counters could be hidden under the hand...