Wow, what a series of questions. Underhammers are considered the most accurate form of target rifle, for many subtle reasons. As for accuracy, you can expect the gun to shoot was well as you can aim iron sights, within the range limitations of the ball, or bullet. For open sights, that is generally 2.5-4 inches at 100 yards. With aperature, or peep, sights, that is 1-3 inches, for a 5 shot group at 100 yards. With a scope you can put 5 shots in one hole on good days.
Chunk gun shooters are among the most demanding of BP rifle shooters, because they shoot one shot each at 10 targets, and the winner is the guy who shoots the shortest string. The range of the matches is traditionally 60 yards. This year's Sgt. York Memorial Chunk Gun Match winner had a string of about 3.3 inches for the 10 shots. That would mean his average shot was no more than .33" from the center of his target.
Depending on the ranges being fired, target shooters like the .40, and .45 caliber rifles, because they are a good compromise between recoil and velocity, weight of ball and wind drift problems. If you stick strictly to conicals, then a .40 caliber rifle with a fast twist designed to shoot conicals will give you extraordinary accuracy out to 100 yards and a bit beyond, provided that you don't have too strong a cross wind.
My recommendation to you is to buy a " first rifle " in percussion, .45 caliber, and whatever style appeals to you. There are Hawken, or " mountain style " rifles out there at reasonable prices. The barrel lengths are about 32 inches, which makes for good off-hand shooting. Stick with the barrels that have a 1:48 ROT for rifling, and shoot round balls with patches. They are cheap, and until you get accustomed to shooting black powder, and climb the learning curve more, this will be a good rifle to get you started, and will retain its resale value if you decide to sell it for something different.
Find a local BP club and attend the matches, and look over the guns. Talk to the shooters during breaks. Accept their invitations to shoot the rifles. Watch what they do to clean and load the guns. Ask Questions like a 3rd grader. Don't be embarrassed to ask " stupid questions ". The only really stupid question is the one NOT asked! You might find someone at such a club who has a good used rifle to sell, and will make you a good deal, saving you more money. Better, he will be able to tell what load the gun likes, and save you lots of time and money getting the gun to shoot. If something doesn't work right, you have someone who is intimately familiar with the rifle to call for help.
Welcome to the forums, and best wishes on your journey of discovery. Enjoy! :grin: :thumbsup: