Well as far as factory ammo, I used to have a 336 that would shoot 1"MOA at 100 yards with Remington 150 cor-locks. Winchester and Federal were in the 1.5 to 2" range, who knows why. That being said I still prefer the 170 grain slugs more but used the 150's for the accuracy. I now have dies and bullets in 150 and 170 . At some point I will get around to working them up.
For 336s in .30-30 or .35 Rem, I have not seen any factory ammo that shoots with better accuracy than the Hornady LEVERevolution. In my current 336, it hovers right at 1 MOA at 100 yards (.35 Rem). Stupid accuracy for a 20 inch Micro-Groove barrel. But..... The FTX is a fragile bullet, best suited for whitetail and the like.
General (all-purpose) use in the woods:
Gotta agree with Core-Lokt. Cheap, consistent accuracy (albeit a little down from the LEVERevolutions). Just don't expect one-shot kills on a big black bear.
Get a heavy-for-caliber hotrod from Buffalo Bore. Expect the accuracy to slide out to 1.5 - 2 MOA, and the recoil to suddenly be noticeable. But also know that you can expect "Bang-Flop" from anything that you responsibly shoot at.
I bought my 30-30 back in the mid 90's. I wasn't reloading then, so I bought a couple boxes of 150gr Winchester ammo. They worked fine in both accuracy and performance, so I bought a few more boxes. Since I just hunt with it and not pleasure shoot, I still have about a box and a half left. When it runs out, I have brass, 150gr Speer HC and several powders to start with.
This! You will have to try as many of the recommended choices listed that others have had good results with. As you've noted, two rifles of the same model can shoot differently with the same ammo. Just a trial and error thing most of the time. I've had good luck with Winchester Super-X 150 gr. Power Point. Good luck finding ammo to try!
I tend to stay away from the factory loads. I've had various performance from them, and I like the ability to tune the rounds to the hunting situation and my gun.
My 336A loves the 160 grain Hornady FTX over a full charge of LeveRevolution powder. If I'm hunting the cotton fields, I feel comfortable with taking 200-250 yard shots without worry. My brush gun Winchester 94 eats does well with a 170 grain True Shot hard cast gas checked pill over a charge of Accurate 5744.
My JM prefers: Hornady Lever Revolution (160 grainer) first and then, Remington 170 grain over the 150 same. If you reload cast remember that Marlin microgroove is OK, you just have to size somewhat larger--mine likes .312+ (gas checks and lubed during sizing). Still scary accuracy from a levergun.