You can start a representative Mauser collection with very few rifles. Once assembled, this collection will show you the thought processes of Paul Mauser as he refined the very-basic 71 into the world-famous 98.
The 1871 was a black-powder single-shot which was made primarily in Germany but also in Austria and England. The original German ones are cheapest and they are identical with the rifles sold to Siam and to China. They also were sold all over the world. Uruguayan Daudetau is a mod of the 71 Mauser to a 6.5mm. 71s were issued heavily to German Colonial troops in WW1 and a few served as late as 1945 with the Deutsche Volkssturm.
71/84 is a tube-mag development of the 71 into a repeater. The magazine was heavily-inspired by the Austrian Kropatscheks which were in service with the French Marines. In addition to German military use, large numbers were sold in 9.5mm to Turkey and it became the foundation of the Serbian Koka. A number of these were smuggled into Ireland by submarine before the Easter Rising. Many were sold here both before and after the Great War and, at one time, there was a .43 Mauser behind half the kitchen doors in Western Canada.
The 1888 was built on a developed/modded 71 bolt system, including the now-standard Mauser safety but with forward lugs added. As built, it used a Mannlicher clip but this was modded into a Mauser Charger before the Great War. Huge numbers went to Turkey and most of the unscrood 88s in Canada today are Turkish milsurps which served from about 1890 through the 1960s. Many of these were sold in China and it was built there for many years as the Hanyang rifle, without the Schlegelmilch barrel-jacket.
The 1889 was the rifle that Mauser thought Germany should adopt. Pure Mauser with the barrel-jacket, charger-loading, 1-piece bolt, Mauser safety. It was adopted by Belgium, which formed the FN company to manufacture it. Modded as the 1890, a bunch went to Turkey.... and a few survive today. 1889, 1890 and 1891 all used a ####-on-close bolt as did the next series.
The 1891 was a basic 1889 bolt with a few mods, extractor in the boltface (think Remington's "3 concentric rings of steel" ads from the 1960s), ####-on-close, charger-fed. The magazines on the 1889, 1890 and 1891 were blatant infringements of the Lee patent. Mauser developed this mag into a type entirely inside the rifle, thus infringing the Lee patent in a different way, added the long-claw extractor and called it the
1892...... which was bought by Spain, developed quickly into the 1893 (Spain and others), then into the 1894 (Brazil and others), the 1895 (most of South America, Oranje Vrei Stadt, Zuid Afrikaans Republijek and many others).... and into that little 1894 Carbine and the very-similar 1896 Swede (high cocking-piece for easier manipulation). 1890 through 1896 all featured charger feed and ####-on-close bolts, were solid, workmanlike rifles and could be quite astonishingly accurate. There is a high amount of parts interchangeability among this entire series, so likely they can be represented with a single rifle.
Then came the 1898, to which was added the third (safety) lug, 3-position safety/disassembly and the last word in controlled feeding. It also featured a reversion to the 1871-type ####-on-opening bolt, but with all the improvements of the previous 27 years. GEW 98, Kar 98aZ, Kar 98b, KAR 98K, vz-24, FN-1924, Chilean 1912, Brazilian 1908 and 1935 and so many others ALL are 98s.
Everything else (stocks, barrels, calibres, receiver rings, action lengths et cetera) is subsidiary to the designs of the ACTIONS. It forms a very clear development path when you compare the series.
So you need 1 of each of those, plus a P-'14 or M-1917..... and you need a Remington Model 30 and a Winchester 54.
And a 1903 Springfield, a blatant ripoff of the 98 design, muddled with bits from the old Krag and a 547-yard zero. Oh, the Americans PAID for that..... in gold. And blood.
But that's the basic series.
Good luck!