The new "traditional" is still generally line art, but that line art is usually done using vector tools that are (output-)resolution independent and can scale "infinitely" without any reduction in quality save on the lowest line screens.
That said, it is also still traditional to have, e.g. the full logo, a 1-color version, a knockout version, and possibly a special full-color version for use on colored backgrounds.
Often, these versions are just layers that can be toggle on/off using layer visibility overrides in, for example, inDesign, but for "office worker use" you will still need to provide them as individual files.
If your logos are more like your avatar, then you will probably want to identify the most likely set of sizes and then export them at those sizes and color sets for people to just drop them into their Powerpoint etc. As you probably know, the "old traditional" way was to have a sheet of clipart with several sizes for paste-up, now you just need to save each size individually, with a file naming convention that makes sense (e.g. the 1-inch version might be "client-logo-cmyk-300px.foo"). You want to avoid your client having to resize the logo, since you would be providing them as raster images (not-vector) and you will be fixing the resolution at creation.
Don't worry about "dpi" or "ppi" setting, just make sure the pixel counts are correct. The rule of thumb for continuous tone photography is 300dpi and for line art 600dpi (minimum). What this really means is that for 1 inch printed, you need 300pixels (or 600 for line art). In my file naming example above, I would know that the logo is full color and is meant for 1 inch.
In the non-vector case, consider using a Single Lens Reflex (SLR) digital camera rather than a scanner, and try and capture the individual sizes using the lens zoom if possible. Zooming with a lens will ensure that the data is captured for that size: sizing after the shot is taken (aka Digital Zoom) is always lossy. I even use a light box and a DSLR when I "scan" 4x5 transparencies anymore.
I also use RAW which allows me to edit the "white point". In many DLSRs, the JPEG/TIFF files they produce have the white point "baked in." With RAW, the capture data is saved separately from the color correction. My lights don't match any of the typical presets, but by shooting RAW, I can make adjustments and then save that set of adjustments as a preset to make a uniform adjustment across the whole set I just took.
As far as color fidelity, you need to look into calibrating your monitor and also checking that the color you get when printed matches within reason your expectation based on your screen. This is usually a little bit of calibrating and then comparing final printed product against your monitor. Once you have some trust there, you can then use that monitor to make color adjustments on your imagery and have better confidence.
Bear in mind that if your clients do not set up their jobs properly, or use good printers, then the color fidelity may be out of your control.
