So I decided on the target of 300dpi on printing and a 5"x7" size for
most of the slides. I will scan at the calculated resolution; I figure
a scan resolution of 1700 that would result in a 10meg files.
I'm still fighting with figures ;-) dpi, pixels, screen, print, in
scanning even mixing that with figures related to my Canon A70.
(megapixels)
The image from the camera is exactly the same thing, in that its image is
also dimensioned in pixels. Your camera menu likely has choices of
creating a few different image sizes (pixels), like full size, 1/2 size, 1/4
size, etc. The scanner also creates images dimensioned in pixels, and its
scan resolution (and size of scanned original) is the menu that determines
the image size. Scan 3 inches at 300 dpi, and you will create 900 pixels.
But after you have either one of these images dimensioned in pixels, then
it's the same thing, regarding use of that image.
Printing the 5 inch width (in the 5x7 inch goal) at say 300 dpi on paper
implies the need for 1500 pixels in that dimension (in whatever way these
might be created). Creating 1500 pixels by scanning say 0.9 inches of 35 mm
film width implies 1500/0.9 = 1667 dpi scanning resolution. Which is
precisely correct (ignoring any cropping issues). This method does of course
work, and it will likely appear as a fine result, good enough.
Specifically, this is exactly what your scanner software does where you
specify to scan at 300 dpi at say 555% scale... it scans at 300x5.55 = 1667
dpi to create sufficient pixels, and outputs this image scaled to print 300
dpi 555% size (the 5x7 inches), which is what you asked it to do. This
little calculator is very convenient.
However there are other considerations too, which some people like to worry
about. One of those is the belief that the scanner can do best when
scanning at integer divisions of its maximum optical rating (in the same way
the camera offers its size choics). For a 3200 dpi scanner, that would be
3200 dpi, 1600 dpi, 1067 dpi, 800 dpi, etc. The scanner only has the 3200
dpi sensor, and so must resample this 3200 dpi horizontal scan line to
create any smaller value, and the integer divisions are an easier resampling
job, which comes out best. Some scanners offer ONLY those integer division
choices for this reason.
So if you scanned this case at 1600 dpi (3200/2), then print the five inches
at (1600 dpi x 0.9 inches) = 1440 pixels, divided by 5 inches is 288 dpi
printed on paper at 5 inch size. And 288 dpi is plenty, it will be fine.
We only need to get near the ballpark of 300 dpi, there is no significance
of 300.000 dpi. We might debate if we can even detect the difference in
plus or minus 30%, but it really wont be any big deal. Normally when you get
to half, it may become apparent.
That often works plenty well enough, and it is often convenient. However
this method sometimes leaves some uncomfortable situations when we cannot
get near enough to the 300 dpi goal (however we may decide it). For example,
scanning at the next higher integer division might come out too high above
300 dpi for our case.
Choices then are still a few:
1. ignore it, and print the larger image anyway, at say 462 dpi. You will
hear a few say their inkjet does best at these large values, but I have
never been able to detect that myself. I cant even imagine it. So I aim for
300 dpi as a reasonable target value for photo quality. It is a comfortable
value (I'm speaking of color, not line art). Anyway, the number is your
choice, whatever you believe that you can see.
2. Scan large and resample the image smaller (to appropriate size, the 1500
pixels) in a photo editor. The photo editor is generally better at this
resample than the scanner (more resources, cpu, memory, software algorithm,
time to do it, etc). A bit of USM sharpening works great after this
resample.
3. Revert back to the first way, scanning at value like 1667 dpi anyway.
It is pretty much personal opinion at this point.
There are two main schools of thought,
A) if I can't see it anyway, pick the convenient way, and
B) I could care less if I can never see it, I want to fight to maximize
every little detail in the most tedious way.
Fortunately, I am very unbiased in this

Actually, I do feel I work
towards a middle ground about it, and do go for those results that I can
actually see. I probably do 2, and sometimes 3, but very rarely 1.