Mosinmaster;
First, what are you looking for exactly? a precision rifle or a hunting rifle? What you're doing here is comparing a robotized CNC machined product against a hammer forged steel hand machined on jigs and fixtures conventional machines.. sort of comparing a Vintage car against a 2012..
Remington is a big company which success depends on MARKETING. The "3 rings of steel" thing is just another selling argument. Remington 700 is a shortcut (improved) version derived of the M-17, which is itself a copy and amalgam of different Mauser designs. I see nothing very special in the Remington design, except that it makes things easier (and cheaper) to machine and there are a lot of aftermarket gadgets made for them (for the same reasons). I don't think they've done any better regarding accuracy / precision than any other major manufacturers - i.e. you can compare their products with almost anything else on the market. The "3 rings of steel" is just like most push feed are; the case base in enclosed in the bolt face ("ring 1"), the chamber is fully part of the barrel ("ring 2"), and the barrel it self is screwed into the receiver ("ring 3"). So, nothing extraordinary in that. I don't say Remingtons are not good rifles, but there are equally and even better actions out there on the market.
Same goes for the "cylindrical" action thing; they found a marketing reason to defend their use of round bar stock steel, which allows less manufacturing operations and eases the stock inletting.... then add to it the free floated barrel and you have a fairly simple to produce rifle.
The "C" and "H" ring thing have nothing to do either with accuracy. Some writers reported "problems" when "H" type actions have the feeding ramp thinned, but in fact the "C" and "H" have both passed hands up any SAAMI or CIP testings. And most "H" type actions are made of alloyed steel, while most "C" type are made of low carbon steel.
In the '60s and '70s, FN offering included target actions and they were as good as any others. I have target rifles based on Mauser actions and I can outshoot a lot of modern rifles and equal a bunch of the "best" with them. Then, unless you rechamber your "H" ring action to a very long cartridge which will be loaded to space age pressures, I can't see any reasons why a M/98 won't stand any normal round against any "modern" rifle.
As for the stock fitting of your specific rifle, I can't say. I guess that when the rifle was new, it went through quality control and passed. Then, it will depend on storage conditions, the woodpiece itself (the grain structure) and the care it got over the years, the action screws tightening and on, and on... You can add if the bedding have moved for any reasons (water / humidity, dryness, loose screws and on and on). Barrel condition is also another point. Barrels are manufactured products and any manufacturer is subject to produce a lemon one day or the other. Then, you have those rifles which shoots anything you feed them with and the same exact twin, which is more than "fussy" with everything. Who knows what you have unless it was first tried? If you're indoubt, just re-bed the action and go from there.
Hope this may help, but your questions are so wide it's almost impossible to give you a precise answer.
