What is best way to transfer an Artists pen/ink paper design to a digital file?

A logo should be a shape that is not very detailed in order to match any criteria of being a logo. So I'm assuming that that is the case.

The way Illustrator's Image Trace works is that it might not produce a better result with a very high resolution image. Quite the contrary. So you might want to scan the artwork in a clean way (no dust etc). Then in Photoshop increase the contrast, but leave some smoothness alond the edges. Do not make very high contrast so that only black and white pixels are left.

Then use Image Trace. It will present you with a warning when the Image is larger then 1500 Pixels Width or Height. For a logo these 1500 Pixels should be enough. If you need more than that in order to catch every detail in your source image, then it is probably not suitable as a logo anyway.

I second Michael's suggestion to redraw it in Illustrator. But before doing that you could try scanning at a very high resolution, the higher the better, at least 800 ppi, but 2400 ppi would be better. 

Clean your scanner first to avoid dust particles.

Place the scan into Illustrator and use the Image Trace command. You may need to adjust the settings for Image Trace. The result will have way too many anchor points, but it would probably be faster than redrawing the logo.

For what you are trying to achieve, I would strongly recommend that you look into an online website, called Vector Magic (www.vectormagic.com), a non-Adobe app. It is an application that transforms jpeg images into vector-formatted illustrations, including Illustrator CC. It can be either a monthly-subscription for $9.95 per month or you can obtain a licence for $295.00, that can work for two machines.

From experience, I have found that it works especially well with heavy amount of high-contrasts. The other observation I would offer is that, if you choose to save your file as an .AI configuration, when opened in Illustrator, the colors of the paths can many times be lesser in saturation than other file formats. To compensate for that, you can take the original file, and upload it in Photoshop, where you can up the saturation, prior to when you put it into Vector Magic.

Sand Patch

You cannot scan dirctly into a vector file; by nature, scans are raster images.  

You can scan and clean the logo in Photoshop, as long as the resolution is high enough, or you can place the scan into Illustrator and redraw it. (There is an autotrace option within Illustrator, but it is unlikely to produce professional-looking results)

Hi.

That will depend on the type of illustration you want to obtain.

Typically, you scan (or take a photo) of the illustration, clean up some blemishes in Photoshop and then drop the file into Illustrator to use Image Trace.