- It seems that 180 PPI are needed for a good print, so if you have less it's probably worth upscaling
In my view, it always helps to 'upscale' to the native output resolution. It will allow to do sharpening at the pixel level, and thus maintain smooth gradients, yet sharpen edges (and add pseudo detail in the shape of noise).
- Whenever you scale you need also to sharpen, downscaling can cause aliasing artifacts.
Deconvolution sharpening also works to reverse some of the blur that's introduced by upscaling/interpolation.
- The image needs to be sharpened for printing, to compensate for the expected degradation of image quality on printing, like error diffusion dither and ink creep. The sharpening needed is depending on the printing process.
These degradations all take place mostly at the output pixel level. Yet another reason to upscale before sharpening.
Beyond what can be recovered by deconvolution sharpening, it can be beneficial to use dedicated software to do the upscaling. I've never liked the posterized look of Genuine Fractals (now renamed to Perfect Resize), but at least it now allows to add noise to cover up the posterization and tune the exaggerated edge sharpness (there's a disconnect between feature sharpness and edges pretty easily).
I do like the capabilities of Qimage for on the fly upscaling as it feeds the printer driver (or writes to an output file), and Benvista's Photozoom Pro, although with the latter one also needs restraint with the edge sharpening (which is possible because the amount is tuneable). Another possibility is Blow-up, but I don't like the artifacts from rounding off sharp corners.
Regarding downscaling, the right way to do it is to blur the image very slightly before downscaling and than sharpen to compensate. Both blurring and sharpening would be made using small radius.
When the downscaling is significant, the pre-blur radius must increase proportionally. When e.g. pixels in the resulting image are a weighted average from say 3x3 pixels, then the blur radius can affect at least 9 pixels in a semi-circle without hurting resolution. Unfortunately one needs to consider that the effect of a less than optimal blur like Gaussian blur extends beyond it's radius. My rule of thumb is that for each downsampling factor (e.g. input/output=3x) the Gaussian pre-blur radius is multiplied by that same factor (e.g. 3x0.25=0.75).
Sharpening after downsampling is then done with a very small radius, since we probably have pixel perfect detail.
Cheers,
Bart