You might use color labels and assign them on import (assuming you import by file type).
The color labels are the most obvious indication in the Browser (and, less so, in the Viewer) of _something_. They are easy to see and easy to apply or change. What you map to the color labels is up to you. It should be something of top-most importance -- something you need to be able to tell at a glance. (Logically, you have to deal with having eight labels, and being restricted to assigning one and only one label per Image.)
I use color labels to indicate the current status of each Image's development. For you, the file type of the Image's Original might be more important. For me, just to give an example:
Color Kirbature Label
Red Develop! ✬
Orange Developing (not completed) ✣
Yellow Bracketed by Exposure Set/Replaced by Externally Edited ❊
Green Developed ✯
Blue Version for Sale. Final! ✼
Purple Detail of Developed ❃
Gray Abandon (but keep) •
You can create your own custom Metadata Tag "Filetype".
The "Gears" icon at the bottom of the Metadata panel allows to manage and add Custom tags.
So add your own field "Filetype" and set this to "Tiff" or "Raw" using batch change.
To quickly find all raws or tiffs use a smart album with the added rule: "Filetype is ...."
Only, you cannot search for jpeg by filetype. Search for Filetype is "Other" and "text contains jpeg" or a similar rule.
I went into the panel for MetaData Customization and added a field called NIK. Because the plugin I use is the NIK Collection. However, even though NIK now appears in the List View of MetaData as a new field, how do I configure the program to fill that empty field for images that have the TIFF extension in the file name?
Or, do I instead just rely on Keywords and add Tiff to that?
While all the suggestions so far are good in their own way they all require you to manually do something.
Using the file name extension requires no further work on your part, it is there as part of the OS.
And of course the best way to do this is yo use Aperture's built in ability to filter on file type. So you could have smart folders that contain nothing but tiffs or jpgs or whatever. Combined with other filter elements will allow further customization.