Bullet type depends on the twist rate. Slower is generally for a patched ball, faster for conicals. But there is some overlap. You'll find a lot of guns made today with a 1:48 twist. Generally good for a ball, and can also be good for conicals, depending on the bullet.
My Lyman Great Plains Rifle has a 1:60 twist. Pretty slow, meant only for patched balls. They also make the Great Plains
Hunter. Looks the same, but has a faster 1:32 twist with shallower grooves intended for conicals.
With a 1:48 twist, you can shoot patched balls well and will probably get good results with a full bore size conical, like this one (it has some lube on it):
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Then there are conicals of more modern design that are smaller than bore size and you use a plastic sabot, like these:
Attached File
Attached File
They're mostly intended for inlines, or traditional guns with a fast twist, like the Lyman GPH I mentioned above. They can also be used in traditional guns with a 1:48 twist, but accuracy will depend on bullet design and weight. You have to experiment.
From your comments, it sounds like you would be happiest with a Hawken type half-stock rifle. T/C no longer makes theirs, so you'd have to shop the used market if you want one. Pedersoli makes a couple of versions that are historically correct and very nice, but they're pricey. A good place to start is with Traditions. They make the Hawken Woodsman. Good rifles with a reputation for being good shooters, and not too expensive.
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https://www.midsouthshooterssupply.com/item/00139r24008/half0-caliber-hawken-woodsman-percussion-28inch-blued-barrel-hardwood-stock
There's also the Lyman Trade Rifle. Another one with a good reputation:
Attached File
https://www.midsouthshooterssupply.com/item/000156032125/trade-rifle-50-caliber-percussion-complete-gun
These guns are good shooters with a patched ball and full bore size conicals (but you'll have to experiment with different bullet weights to determine what shoots best in your rifle), and maybe with some modern bullet/sabot projectiles (I don't want to try to elaborate on that because I'm a traditionalist, I don't shoot those modern projectiles; so I'll let someone with more experience elaborate on that).
A steel range rod is a common sight at the range. It's easy to work with, you can use a brass muzzle protector with it, it's very strong, easier to pull a bullet with if that's ever necessary, and it saves wear and tear on the gun's wood rod. I usually use one at the range. You can do that and save the gun's wood rod for the field, or not. It's up to you.