Miroflex, one thing you might consider is attending a match, to see what people in various classes are shooting.
Regarding an M98 action, here's what Stuart Otteson mentions in volume 1 of his Bolt Action Rifles books:
The M98 receiver beds on the flat underside, principally behind the recoil lug and at the rear tang. The front surface has about 1 sq. in. area. This is relatively small in comparison with most later bolt actions, and the Mauser is, in fact, not noted for maintaining a solid bedding in the stock.
This would tell me that you may have some work to do, playing around with bedding, if you are going to enter matches against newer designs.
Vertical guard screws thread into the recoil lug and tang. Both are bushed to prevent springing the receiver or floorplate. Nevertheless, a long slender tang and the deeply notched left rail leave the Mauser receiver weak and easily bent by guard-screw tension if support contact in the wood is im- perfect .
and . . .
The left siderail is cut out to form a deep thumb clearance just forward of the bridge. The primary function of this notch is to aid clip charging of the magazine, but it also creates a gas-release point for the left raceway (D.R.G.M. 56,068 issued Aug. 9, 1895). When clip charging is not a factor, the desirability of this notch becomes suspect, since it does seriously weaken the receiver mid- section.
This problem has more to do with fitting a heavy barrel and supporting it when it is free-floated. However, the flexibility will affect bedding, as mentioned above.
Performance of the M98 lock can serve as a basis to compare later turn- bolt designs. Its mainspring gives a moderate average driving thrust (about 17 Ib.) over a fairly long distance (about ?hin.) to achieve a high energy and impulse blow (about 130 in.-oz. and 1.4 oz.-sec.). The significance and relation to performance of these parameters is covered in later chapters.
Lock time is just over 5 milliseconds (ms.), slow by today’s standards, yet very good in its day. In fact, compared to many non-turnbolt type actions, it was exceptional. Even today’s automatics, pumps, and lever rifles, with their swinging or hammer type lock mechanisms, usually can’t match it.
Like many other authors, Otteson addresses issues that are more of interest to sportsmen, while a few of his comments, like those Iv'e quoed above, relate to target shooting.
You must also consider the condition of your bore and your trigger Your sporting barrel, especially if your competition requires fairly rapid multiple shots, will work against you if you face folks using heavier barreled guns. This will also require fine-tuning your bedding. At some point, you may be required to consider how desirable modifications are to a nice, valuable rifle. Or, you could consider getting another stock for competition purposes so you can play with the bedding (glass bedding and pillars, for instance) without modifying your existing stock.
This isn't to say that an M98 action will not shoot, because many shooters over the years have made them shoot well. But it is something to consider.
But el jefe has, in my opinion, "rung the bell" when he mentions ammunition. Getting any kind of ammunition is one thing, and reloading is ruled out. A lot of 7x57 mm ammo is intended for sporting purposes and often is held to pressure levels that are appropriate for using the ammunition in surplus rifles that have a 0.318" bore. The barrels of 7x57 mm rifles are often cut with a long throat, so as to chamber the long 175 gr round nosed bullets that were often the standard military load. You might consider whether these bullets and the chambering are going to work for your intended purpose. Granted, with all of this said, you may have a combination that will, despite all, launch bullets into a pretty respectable group. Knowing what the gun will do in a simulated competition test is probably your first course of action.
But as el jefe noted, 30-06 ammo is probably going to be easiest to find, especially in bullet choices that are more amenable to your chosen use. The Blaser-derived rifle is modern and should provide the basis for a pretty accurate rifle. Frank de Haas, in his bolt action book, reported that he was able to achieve "less than .750 MOZ" at first, and a little over an inch with repeated shots with his Blaser 22-250. He then mentioned that he achieved "less than .500" for a three shot group from a cold barrel. I suspect that this would be more along the line of what you're seeking, as compared to an M98.
However, maybe it would be fun to bring the old Rigby out and give it a try, to see what kind of performance it could turn in for you. It might be fun, tinkering around with an old rifle like that, and also it could well be fun stepping out onto the range in a competition setting. Who knows how well you may do?