In my experience, there is no particular significance to the number of grooves in a rifle barrel, and no demonstrable advantage to any specific rifling profile, though barrels intended for patched round ball or picket bullets will likely perform better with 6 to 8 grooves of equal width to the lands or a bit wider, and not more than, say .010" deep. Fewer or more grooves offer no advantages in performance, and may actually be less accurate, or complicate the process of finding a patch and ball combination which works properly.
The important factors are the quality of workmanship in the barrel, and, to a lesser extent, the material of which it is made.
A good barrel MUST be smooth as to finish on lands and grooves, without burrs or rough patches, consistent in pitch, and uniform in diameter of bore and grooves from breech to muzzle, with a slight choke or taper being permissible, but not necessary.
Rifling pitch is another topic, and has been extensively discussed previously - the best procedure in ordering or selecting a barrel is to consult the maker for his recommendations. Exactly whose barrel to use is also a topic for discussion with other users, and also open to endless debate.
I am a barrel maker (re-retired), so offer my opinion based on experience, having made a VERY wide range of custom barrels to meet individual requirements, as well as the tools used in the manufacturing processes.
If you pick a reputable barrel maker, consult with him on your requirements, and follow his recommendations, you can expect good results. Advice on all other topics relating to good shooting is available from members of this forum and others like it.
mhb - Mike