It sounds like you are making all of your image adjustments (contrast, color cast,cropping) using the scanner and scanning to obtain a file for printing. In this case the DPI in you final file should be equal to the DPI of the printer device. It can be a bit larger (360 DPi instead of 300 for instance) because the printer software will downsize the DPI. This is much preferred to having the printer software upsize the DPI. In one case excess information is simple discarded (averaged actually) but in the other. the software algorithms have to create something out of nothing.
I would suggest a different workflow. Scan to make a digital negative that can be used for any purpose. The output dimensions (36mm X 24mm) of the scan will equal the negative size. Then you set the scan's PPI, not DPI. This approach is much more flexible and in principle you only have to scan once. Also post-processing software such as Photoshop, Lightroom and others is superior to scanner software for the same purpose.
For proofs I scan 35mm film at 1200 ppi and 16 bits (10.8 MB, 1.9 megapixels). This size scan is suitable for on-line viewing. Sometimes 2400 ppi scans (43MB, 5.4 megapixels) are useful too
For prints (8X10 or arger) I rescan at 4800 ppi/16 bits (~170 MB, ~30.6 megapixels).
I use .tiff files and scan B&W and color the same way.
The more you adjust a scan in post-processing, the more data you should collect. A 16 bit scan will suffer less from inevitable digital roundoff errors than an 8 bit image.
When you are done adjusting the image, you select the print size, the DPI appropriate for the printer and save/export the file as an 8 bit jpeg. I email my files to a local lab for printing. They want 300 DPI files. I sometimes send them 400-500 DPI files and trust the printer software to down size the DPI.
Shutterflower brings up an important point when he mentions that different negatives have different minimum requirements for scanning. That is, the less information in the negative, the less information you have to digitize to best represent the original. ISO 50 slide film is capable of recording more information than ISO 800 negative film. At the same time, a city scape on ISO 50 slide film on a perfectly clear day will have more information than a a seascape taken on a foggy morning using the same film and lens. The problem is, I am not aware of any software that evaluates the information content of an image. So, I collect the most information I can when I know an image will be printed at 8X10 or larger.
willie