Look at Wideners.com & see if they have the "Lee Anniversary Kit" for like $38 or so. You get a single-stage bench-mountable press, PLUS a Lee Reloading Manual which had ALL KINDS of reloading data for lotsa cartridges that I didn't even know existed. It's a VERY comprehensive. It also has sections on cast bullets and some "how to" stuff kinda "hidden" among other sections.
Lee Dies in the red plastic container are probably your best buy. They come WITH a shell holder, some limited loading data, and a powder scoop. There are better dies in the world, but they're easily twice as expensive, and they're NOT twice as good.
There's a Lee Priming product (technical name evades me at the moment)) that screws into the top of the loading press, where the reloading dies usually go. It is fairly inexpensive, tough as nails, and a very precise method of priming cases. The downside is that it can be frustratingly slow. If memory serves, this item uses the shell holder that came with your dies.
As soon as you get extra $$, you'll want one of the "hand primers" that Lee or Lyman makes. For the love of HEAVEN, get the one that uses the shell holder, used in your reloading press. ONE of these manufacturers makes a hand-primer that uses its own special kind of shell holder, and they're a mess to keep track of. Avoid that type.
Measuring the powder charge is your next major hurdle. I don't see a way around a good electronic scale or a beam-balance type scale. The electronic ones are faster but more expensive. I haven't used any of them enough to advance an opinion on what's good vs. useless, but BOTH varieties exist on the market. Ask around & choose carefully.
Almost everyone makes good balance-type scales (I don't know of any really BAD ones out there). These are perfectly adequate for measuring your charge weights to within 1/10 grain, and you don't REALLY want to split hairs any finer than that, for now.
METERING the powder charge can be done with either an adjustable powder charge thrower, or a set of volumetrically calibrated powder scoops. The former are @ the same price as one or two new reloading die sets from someone other than Lee. These charge cases rapidly, and are more than acceptably precise. But the combination of these attributes is expensive.
Lee Precision sells a set of 10 or 12 powder scoops, with a sliding-card index of how much of a particular powder each scoop throws. The last time I looked, the whole thing was less than $20. With a little practice, a reloader can charge cases with the scoops as fast as with the charge thrower and with the same accuracy(some believe the charge weights are MORE precise than from a charge thrower). The disadvantage is that there is less flexibility in charge weights. If one starts at a charge weight of 47.0 grains, and wishes to change it by 0.1 grains, there may or may NOT be a scoop or combination of scoops to deliver the new charge weight. Even so, metering powder in this way beats the heck outta NOT reloading your own. Four or five boxes of factory 8x57 Mauser Ammo will probably buy a very good powder charge thrower. Forster makes the best one I've ever used, but they are quite expensive. If you're not planning to shoot in match competition, it'd difficult to justify the cost. I have the most experience with RCBS and Hornady/Pacific charge throwers, and they're absolutely fine for most purposes. I bought and tried one Lee charge thrower, and didn't like it. Since Lee is the champion of volumetric charge metering with scoops, I'm not surprised that not much trouble was spent on charge throwers that depend on a scale to keep them honest.
Almost any Rifle powder that works in the .308 will work in the 8x57. If I could choose only one powder for all rifle calibers, I'd want Hodgdon H4895 or IMR 4895. It is as versatile in rifles as Hercules (Alliant) Unique is in pistols. And works at least adequately (usually much better) in cartridges ranging from .222 Remington to 7mm Remington Mag.
4895 also has another neat advantage. It has a very broad range of charge weights that can be used without concern serious concern for maintaining high charge density (i.e. getting the case as full as possible). If one wishes to make lower power, lighter recoiling loads but maintain the same bullet weight, usable loads can be made by multiplying the charge weight for "full power" loads by 0.60. Thus our example "47.0 grains" charge weight becomes 28.2 grains for the lower-power loads. How much the lighter charge reduces velocity is something pretty specific to the rifle, but don't expect it to be very close to linear. If a 47.0gr/H4895/150gr. Spitzer load chronographs out of your rifle at exactly 2800 f/s, don't expect that the reduced 28.2gr/H4895/150gr. Spitzer load will chronograph out of your rifle at exactly 1680 f/s. It MIGHT, but then again it might NOT. BUT... I would expect that such a reduced load might clock somewhere between 1500 and 1850 f/s. I would also be VERY surprised if the load velocity was less than 1350 f/s or above 2500 f/s.
Okay, it looks like you got "watch-building instructions" when all you REALLY wanted was to know what time it was. But I'd rather provide you with too much information than not enough. You can always ignore what you find (by experimentation) not to apply to your situation.
Best of luck.
