Simple question, complicated answer, because the Mauser was such a popular action that it was widely distributed and copied - indeed, most modern bolt actions (with the exception of the multi-lug bolts) are modified/simplified Mausers designed for easier manufacture (i.e. cheaper).
Mauser went through a series of models. Prior to 1893 all their models had a protruding magazine except for a couple black powder models which are mainly of historical interest.
The 7x57 cartridge was actually introduced with the 1893 Spanish model, but the last, and best, Mauser was the Model 98, which was made in large ring (receiver diameter 1.4") and small ring (receiver diameter 1.3") versions. Usually you can tell the difference between large and small ring receivers by looking at where the ring joins the left sidewall - with large ring receivers there is always a step-down to the left sidewall, whereas with small ring receivers there usually is no step-down. The one exception to this that I am aware of is the highly prized Czech VZ-33 and G33/40, which do have a little step-down. The large ring Mausers are considered better for magnum cartridges, but either large or small ring is quite adequate for the 7x57, and the small ring is a couple ounces lighter. There is also an intermediate length action which is about 1/4" shorter than the standard 98 which is well suited for the 7x57.
The Model 98 was originally produced by Germany, but sold and adopted by many other countries. It is the model that gunwriters mean when they refer to a "modern" Mauser action. It was built not only in Germany but also Czechoslovakia (Brno/CZ), Belgium (FN), Yugoslavia, Mexico, etc. It is a strong action not because of its metallurgy, which is carbon steel, but because of its design. Properly adjusted it is one of the most, if not the most, reliable actions, with excellent gas handling in the event of case rupture, which used to be more common than it is now. Its large claw extractor and fixed ejector system are the comparison standard.
As a sporting action, its drawbacks have to do with its bolt handle and safety, which in unmodified military form are poorly suited for scopes (remember that when it was designed, rifle scopes were basically non-existant), and its direct acting double-stage trigger, which while simple and reliable, is heavier than many modern riflemen would prefer. These are the areas where most modern Mausers are modified. In addition, in many modern Mauser actions such as the FN (Belgian) and Zastava/Mark X (Yugoslavian) the left side of the internal receiver collar is milled out as a production shortcut, which compromises gas handling, although the likelihood of cartridge rupture in modern ammunition is very low, so it is more a theoretical risk than a practical one.
So, good modern modified sporting Mausers include:
FN (Belgian) - also the basis of some J.C. Higgins, Western Field, Browning, High Standard, and early Husqvarna models. The Browning and FN versions are somewhat pricy, the Husqvarnas (model 640) a little less so, the private label brands, e.g. J.C, Higgins (Sears) and Western Field (Montgomery Ward) least expensive.
Zastava (Yugoslavian) - Interarms Mark X, Remington 798, more variable in quality than the best actions
Brno (Czech) - 21H/22F (small ring) and ZG-47 (large ring) - pricy particularly as collector interest increases.
The Husqvarna is a special case, because early post-WW II rifles were built on FN actions, then Husqvarna developed their own (small ring) action on a modified 1896 Mauser action, which does not contain a number of the safety features of the 98 Mauser but because of its superior steel is considered as strong as any modern action.
Some military Mausers (can be sporterized with modified bolt handle, aftermarket trigger, low scope safety) include:
GEW 98 (large ring German)
VZ24 (large ring Czech)
Argentine 1909 (large ring, made by DWM in Germany, prized for its exceptional finish and trigger guard bow floorplate release)
VZ33 and G33/40 (small ring Czech)
98a carbine (small ring German)
1910 and 1936 Mexican (small ring Mexican) - designed for the 7x57 cartridge, slightly shorter action than standard 98.
For reading material, Ludwig Olson's "Mauser Bolt Rifles" (available from Brownells) is considered the standard text.
Another good reference which covers many bolt actions including Mausers and many others, is Frank de Haas "Bolt Action Rifles"
