I use 28 lb. all-cotton paper, and a v. pale blue as a personal touch, so that it stands out a smidge from all the others. Cream is also a nice alternative to white. I wouldn't get any more "unique" or "distinctive" than that ...
I like to use paper that is heavy enough that it feels good in one's hand, but not so heavy that it stands out or draws attention to itself for that reason, as llg noted (hey there, girlfriend!!

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