Well, there are three main types of brushes...
"Brass" (actually phosphor bronze) brushes are the norm - they're soft enough to not damage the bore, yet stiff enough to work out powder and copper fouling.
Stainless steel brushes work incredibly well in removing even the most caked in fouling, but since they're made of a harder material than the bore, they leave microscratches in it. (except Hoppes' Tornado brushes
which use the edges of a helix shaped brush to clean instead - these work very well and are non- or not very damaging).
Nylon brushes I've never really had any luck with... they're good to use with copper solvents (since phosphor bronze brushes get eaten by the solvent) but I find they're either too stiff to easily work the bore with, or too soft to do a good scrubbing job.
The main problem with traditional rod & patch/brush cleaning is the rod... if you clean from the muzzle end... it is very easy to damage the crown, and no matter what end you clean from, letting the rod run along the lands of the barrel is damaging as well. You should really use a bore guide that keeps the rod as centered as possible in the bore to minimize scraping it.
Also, those cheap 3-piece aluminum rods are good for carrying in your field/range box, but they flex too easily for day to day use... I use boresnakes for most cleaning... if I have to do anything that requires a rod, I have Tipton carbon fibre rods for the rifles - thin one for .17 and .22, thicker one for fullbore and a straight steel one for .50 and shotguns.
As for how often to clean - there are as many timelines as there are shooters. I must be doing something right, half the people say I do it too often, the other not often enough.