Re: 8mm rifle
The 8x57 is a fine cartridge, especially when loaded to modern pressures. However, no one is making a match bullet, unless you find a European company that makes them. Price would be a problem though. It will certainly be a thumper, as you're talking about 200 grain bullets.
If you wanted a fine European cartidge with MANY high quality bullets available then you can look to both the 6.5x55 and the 7x57.
Both of these cartridges are excellent, but you must reload to enjoy these benefits, as most American ammunition for both of these fine cartridges is loaded to very low velocities for fear of the rounds being fired out of very weak 120 year old actions.
There is no magic to reloading, but you must be carefull.
Lee, Speer, Hornady, Nosler and others all put out reload manuals that explain the details.
If you do not reload, but want to shoot, the .308 and .223 are your answer. Both have readily available match loads that are relatively easy on the pocket book.
What is your experience level with precision shooting? You seem to be jumping around, from the 8mm to .338 to .50 cal.
If you want to jump into something like a .338 and spend 5 bucks every time you pull the trigger, so be it, but you would be better served with a good, accurate .223 with good glass and 69 grain match loads.