I sent my first mass-mailings out with resume paper and matching envelopes, printed on a laser printer (which I already had). The envelopes are a total waste because they are thrown out before they reach the attys desk, and the paper can go either way. Sometimes they just photocopy it anyway and pass them out to the committee so they won't know the difference. A laser printed page might photocopy a tiny bit better?
I saved a lot of money and time e-mailing subsequent resumes/cover letters as pdfs, which many firms say they prefer. This lets you avoid the whole printer/paper issue and speeds up the process.
However, for in-person encounters it's nice to have resume paper. Probably not necessary but makes a good impression.