Tom Ang’s recommendation on input resolution in his book Advanced Digital Photography:
Broadly speaking, with images of average proportions, images smaller than about 150 pixels long cannot show anything but the broadest structure of a picture. For web use, images generally need not be longer than 720 pixels–which is also adequate for smaller prints (i.e. half the size of an average postcard). For fair-quality prints and output to 8 1/2×11 inch size, you will work in the 2000-2500 pixel range. For good quality work, the numbers rise to image lengths of 3000-4500 pixels.
Adorama lists their recommendations on their print order site.