Many collectors try to find whole subsets of machines.  I've focused on several brands, or makes, that could be considered unusual in themselves.  Here is one whole subset, all made by Nippo Machine Company, Japan.  The related machines are shown below; this page is a lesson in advanced collecting!
Top right, Atlas.  Right, Del Mar.  Above, Elgin Collegiate.
Above, Morse P100.  Right, Argyle P201.
The Nippo machines are licensed versions of the earlier Halberg Traveler, which is a rare machine.  Seen at left.
Halberg sold the design to Royal as well.  Clockwise from above, all carrying the Royal brand name;  early Royalite, Royalite 64, Arrow, Parade, and immediately below, Quiet de Luxe.

The final version, the Quiet de Luxe, is heavily re-engineered to incorporate basket shift, and some other smaller changes, but very much of the original design remains.  None of these is highly rare, but none is overly common either.  This latter variant is the most unusual.
As you can see, truly advanced collectors will try to find out what constitutes a family of machines -- what's related to what, and what's developed from what.  And then they'll try to get them all, or at least one of each mechanical variant, disregarding exact brand and model.  This provides, for many, endless hours of challenge and fun.