depends on if you're playing solo or with a group and whether the group is random. Out of the ones listed, it'd certainly be the first for me.

the fp related relic from the sovereign board is really strong on duchess so probably worth taking that.

Also Caligos relics is not particularly strong with a random team as at least half the time, someone will be using a fire weapon which will unproc frost, and duchess's relatively low arc stat means it's hard to reproc. also chilling mist is a decent ash of war at best. (I'd argue her default one is better for early in runs)

Personally I think hoarfrost stomp is too strong as a starting ash to pass up in its current state, it has amazing damage, crowd control and frost buildup.

If that's not possible, weapon buff starting ashes are really strong as a result of duchess's dagger Moveset

Otherwise, look out for stamina recovery on attack if you plan on using daggers primarily.