Good morning Adam,
Do a little research on the forums here and you'll see numerous threads on the subject.
That said, there are some broad categories of answers for you.
In general, a slow-twist like 1 in 72 from a good maker will shoot well with roundballs, but won't stabilize long heavy projectiles. This worries me not as I only shoot traditional roundballs. These slow twists are very forgiving about shooting well with various speeds and powder charges.
The faster twist rate (like, say, 1 in 48) will stabilize longer projectiles, but will generally be fussier about what powder charge they'll group well with. Like working up a load for a modern rifle. The down side is that your accuracy load may not be where you want to be on velocity.
Others with more experience can correct me here as needed.
As far as type of rifling, I will flatly state that in my experience with both, I'd go with flat bottom rifling. There is no down side to flat bottom rifling. As my competitive shooter friend noted, most competition guns on the firing line at Friendship are flat bottom rifled. While some may say that round bottom rifling is easier to clean up, I can see no practical difference in personal experience.
Round bottom rifling? I think, if folks are honest, they'd say that it looks cooler and looks more traditional. I am not sure anyone will claim that a well-made round bottom from the same maker will predictably outshoot a well-made flat bottom.
The down side is that some makers cut the round groove rifling really deep. Too deep. Again, I think this is so that the round bottom is really obvious to the eye. The big downside to that is that it can be a pain-in-the bore to get it to seal with patch and ball. You have to resort to really thick patching, and then try to cram in a fat ball to drive it to the bottom of the deep grooves. To what purpose? I don't know. It can create a situation where you get gas blow-by cutting on your patches and erratic velocities and accuracy. I had one round-bottom barrel that I never could get to shoot reasonably, even with a 5-under roundball and .020 denim patching. Pain to load too. Blown and gas cut patches all the time. Daryl can give chapter and verse as he helped me try to find a combo for that barrel that would work. I had it rebarreled.
That said, my competitor friend also has a Tip Curtis flinter with a Colerain round bottom rifled barrel. The grooves are pretty shallow. Maybe .010 to .012. It loads and shoots great. The round grooves are not very prominent or deep , and are therefore not very "visually interesting". But it works correctly.
Yes, some round bottom rifles shoot well, and some can be made to seal a ball and patch combo easily. My point is, since there is no down side to flat bottom rifling, save yourself possible misery and go flat bottom. Or specify no deeper than .012 round bottom rifling and hope for the best.
One last thing I'd suggest you at least take a look at: if Green Mountain has the configuration you are looking for, or if you can search one out on the internet, they make a darned fine shooting barrel. Worth a look at least. Not saying anything bad about FCI !
I hope this long-winded reply helps you a little. I'm an engineer by trade, and my analytical brain thinks things through maybe a bit too much.
Best wishes, and God Bless, Marc