You can't talk about 1920s football cards without covering the iconic Spalding/Sports Co. of America set.
The football set is actually a subset of a much larger multi-sport set produced by the AG Spalding company to promote their products. I believe these cards were distributed along with a scrip that could be used as $$$ to buy Spalding products and equipment. There is a lot more info on this set in Carl's iconic football card book: "Collecting Vintage Football Cards". Anybody collecting vintage football NEEDS this book by the way as it's very comprehensive.
If you go out to ebay you will see a BUNCH of cards from this set available but not many of the football ones. In general they are very difficult to find and some are virtually impossible. There are 14 football cards in the set plus a promotional Red Grange card that was only distributed in an uncut salesman's sample so it is very rare. The cards come with three different backs: blank back, ad back, and bio/stats back with ad backs being the rarest. Besides being distributed in 1926, there are versions that have a 1927 copyright on them as well. This is considered a separate set even though the cards are all the same. The 1927 copyright cards are even more difficult to find.
For many of the stars in this set, their cards pre-date their official rookie cards by years if not decades. I've personally never understood the reasoning behind not designating someone's first card as their rookie card but I suspect it was done through a combination of ignorance about earlier sets, the belief that a rookie card must be nationally distributed by a major set producer, and the TPGs wanting to drive demand for rookie and HOF registry sets by choosing cards with higher populations.
Pre-rookies of note in this set include: Red Grange, Ernie Nevers, Benny Friedman, Harry Stuldreher. All are the first cards ever produced for these players except Grange as it is likely his Shotwell cards and his W590 strip card came earlier.
jeff