It's time to clean my rifle but i am a little new to cleaning rifles. I am having a hard time shoving the wire brush tip down the barrel. Just seems to me that it will damage it.. Maybe i am being to cautious with my new rifle but just need assurance that is doesn't hurt anything.

1. I put a patch down the barrel lightly coated in solvent
2. run the brush thru a few times
3. run a patch lightly oiled down the barrel..
4. lightly oil the rest of the chamber and components, ie barrel exterior, etc..

is this correct ???