When you start to think about a flintlock rifle, the first though for accuracy, whether for target or hunting is the lock. Then for accuracy its the triggers. Target shooting for most off a rest or off hand will be better with a set trigger. Double set trigger allow you to shoot the rifle with a comfortable single trigger for hunting or woods walk targets. The very light set trigger is better suited for shooting paper targets or chunk gun matches.
Stock architecture is important for target shooting. What is comfortable for off hand shooting may very well be a cheek slapper when shot off a rest. Then if you shoot prone with the rifle on a chunk of wood (over the log or chunk gun shooting), you may find that the wonderful off hand rifle can't be aligned when on the ground.
Barrels are often quite accurate. Really its the profile that is suitable for the rifle that becomes important.
If you are getting the sense that I am not about to suggest a rifle for you, well you are correct. Your budget will only cover a lock, barrel and stock parts. You still need triggers and all the remaining hardware and the time and skills to build one.
You need to get into a traditional muzzle loading gun club. There you may find a rifle that fits your budget and your shooting needs.
In the mean time, set your $600 aside in a safe place. An assembled rifle that fits your desires will probably cost from $1200 to $1800 and more.