So the Lyman
Great Plains Rifle is a half-stocked rifle, made for Lyman by Interarms in Italy (iirc)
The Pedersoli that I'd recommend is the full stocked
Frontier.
Both come in flint.
They are both good, factory, "entry" flintlocks, having large locks, easily handled, and both have double "set" triggers.
BOTH will slay deer or punch paper targets
Some folks that use these see no reason to go any further. The cost won't break a budget, but if the cost is pushing to the top of what you'd like to pay, then look for a used rifle, or perhaps even a Thompson Center Hawken in flintlock... in good condition with a good bore.
BTW none of the above rifles are super correct for historic appearance, but they will all work quite well as mentioned slaying deer or punch paper AND you won't be turned away from an event for having a flintlock half-stocked plains rifle, nor for having the Pedersoli Frontier in flint. Some events have a "cutoff" date that might prohibit a plains rifle, but that sort of event would prohibit you using a genuine 200 year-old plains rifle..., so....
I know that some of the folks I've spoken with from the Southwest will treat their patches with a Borax and water solution, allow that to air dry, and then treat their patches with lube. The Borax ******* smoldering. I don't know the concentration of the solution, sorry, and one really should try it with the shooter's chosen lube anyway, as some lubes might make the cloth into a sort of "candle" in the grass downrange. OH I do know that you don't do the dried Borax'd cloth patches if you do "spit patching"
You can though douse the dry Borax'd patches with water instead of spit...
LD