I know this won't help a whole lot, but don't be surprised if someone comes along and tells you that it depends on the specific time frame you want within your range, your specific "persona" that you are trying to portray, etc.
If it was me, and if I was in a hurry, I would get a Pedersoli Blue Ridge in .54 that Cabela's has on sale right now for $550, which leaves you a bit of money left over for flints, a mold, etc, but a Brown Bear said, it is a bit generic and there will be some "HC/PC nazi" that will point out all the things wrong with it to you. But that rifle at least gets you a good gun to hunt with and seems at least close to what you would need to re-enact your desired time frame, even if it isn't "perfect". If you want "perfect" and aren't in a hurry, I would say set aside the money you have and save a bit more to get something more correct. But that is only if you are a real stickler for everything historical having to be absolutely perfect. Personally, I'd rather get out in the woods with something acceptable now and then worry about perfecting things later, but if you ever run into me in the woods, I'm liable to be wearing blue jeans while carrying my Lyman GPR, so there's a lot of camps I wouldn't be welcome in.
Welcome to the addiction! :hatsoff: