This is a very complicated question.
I am quite proud of the Paedagogus collection which now numbers 31 editions (be the first on your block to collect them all!), including the elusive 1972 paper interim version.
The framed musical score of "Theta Kappa Nu Girl" hangs on the wall, as do three different Forms 25 from pre-'39 to present.
I was very lucky to obtain a badge made in 1913 by Hoover & Smith of Philadelphia, an old gothic arch pledge pin, and a pearled TKN sweetheart pin (same size as an AM button). Fate smiled on me after I donated a prototype post-'39 pledge pin to IHQ by finding me another one for myself. These have only 3 triangles instead of 4.
But most meaningful are the 2003 Paedagogus inscribed to me from our most recent High Alpha, the 1992 History of Lambda Chi Alpha inscribed at length by Chuck Peyser, and an old chapter newsletter with a blurb saying I accepted my bid January 16, 1972.
Oh, and the Radio Shack hands-free portable Earp-phone for those tri-weekly 3 hour conversations! That's definitely a LCA item!
In ZAX,
Jono