Kenc,
GN has given you some really good advice. I'd like to chime in with a few other comments.
I would highly recommend that you stick with 8 X 57 if your rifle will shoot well after you get the sighting organized. Many of the Turks I've seen appear to have had armory restocks and reblueing, and the one I bought appears to have a *new* barrel. I've never seen a mil bbl *so* clean and sharp. I haven't fired mine (bullets coming in today) yet, but will do so this weekend. If you need info about making an electronic bore cleaner, check this site: Well, drat it, I didn't bookmark it. I'll find it and revert to you later if you need this.
Trigger... good advice about aftermarket (Midway has good triggers on sale right now.. check their websie), but there is a lot that can be done to the Mauser trigger if you're not inclined to spend the money. You can silver solder an extension to the front of the trigger and install a screw and locknut to control sear engagement. However, IMPORTANT WARNING, getting the sear engagement below 5 lbs makes a very dangerous field rifle. It is safe for a bench rifle, and you can get a very good letoff down to abt. 3 lbs. A much better thing to do is to install that setcsrew and adjust it to retain a bit of hte double-stage pull. Now, have a competent gunsmith or gunnut to remove metal from the sear until you get the letoff you desire. Did that make sense? You can safely go down to 3 lbsd for a field rifle with this system, not that I recommend that low a trigger pull for a hunting rifle. Depends on how you are hunting. If you're in locations where all hunting is done form a box stand, then you might as well be on a range :-)
Stock: If you have an eye and talent for woodworking, a very nice looking rifle can be made with the mil stock. If you have one of those nice Turkish walnut restocks, it'd be a shame not to use it. If you'd like some pix of well-done sporterizations, send me a PM. They make a really nice full-stock rifle or carbine. As close as Im likely to ever come to having a Mannlicher rifle :-) A bit of glass bedding at the front lug and barrel cylinder andback at the rear tang, along with free-floating the bbl., will usually give you a bit of improvement in group sizes. Pillar bedding is more complicated, but still easy for the DIY gunnut, and will help accuracy, esp with the heavier cartridges such as the 8mm. I'd leave these mods until you veryify that your bbl will shoot, look for groups of no more than 1 1/2" at 100 yds w/factory ammo, assuming that you have good sighting equip and can hold pretty well. If it will do that, then it is worth keeping the bbl and working on various accurizing methods.
Back to the 8X57. That is a superb cartridge, fully capable of taking any game on the NA continent (or SA, for that matter). Midway has the superb Remington 185 gr CoreLokt PSP for about $14.100. You can't shoot cheaper than that. Also pick up a set of Lee collet dies if you order from Midway (or if you get them locally). These dies are cheap and work a treat. My brother and I have mostly converted solely to these dies, must have 20 sets.
Rebarrelling: If you do, consider carefully your caliber choice. Many think that 6.5mm is the ideal, and it is fast becoming the hot number in 600 & 1000 yd shooting. Buyllet choice is superb, starting with varmint bullets and going to 165 gr RN. Again, it'll do for anything in our hemisphere, though it isn't quite up to use as a stopping rifle for wounded grizzlies. Be sure to shoot your grizzlies from far enough away that you can get in a couple of extra shots before he gets to you :-) All seriousness aside, it is fully competent to take elk and moose. 6.5-284 is the hot number if you like wildcats. Nothing wrong with the 6.5X55 Swede cartridge, or the well -respected but uncommon 6.5 X 57. For these two,if you don't mind wildcats, it costs the same to have the improved ersions chambered and they both offer 150-200 fps greater velocity to the handloader.
Oh, yes, there were at least tow differnt bbl threads, and maybe three (I've heard of another but haven't seen one), and one is exactly like the Rem 700 series. That means that, if you have one of those, there is a steady supply of pulled barrels available. I see 700 bbls at gunshows going for $50-$75. If you live where long-range shooting is done, contact the shooters about who has rebarrelled lately.
Best of luck, and let us know of your project. Oh, yes, Start a journal in a spiral-ring notebook or some such. Record every mod you make and the result, all the cartridge, bullet, and reloading data, along with actual target groups pasted into the pages. You will be amazed how useful this will be.
Cheers/buffler