Newman collectors interested in his Metric compositions would be well-advised to seek out any covers listed in the discography below while vinyl is still available (some independent labels, such as Rhino and Varese Sarabande, have also been approached to release an collection of Newman covers on CD, which would help to share some of the rarer items).
One important consideration for cash-strapped collectors is that the value of most artist covers is typically more influenced by the collectability of the cover artist involved than Newman's own writing credit -- be prepared to pay anywhere from a few dollars for a Vic Dana single up to $25-30 for the more obscure British releases.
Given his respectable fan base (Newman estimates each of his albums to have sold approximately 500,000 copies, with the exception being Little Criminals' 700,000), it is likely that to loyal fans, any of the artist's original demo acetates are the far most collectable entities: expect to pay anywhere from $50-100 or more for an authentic demo. Even better: write the good people at Warner/Reprise and ask them to scour their vaults and issue a fitting box set for one of America's true originals. Supply may just rise up to demand.