You can over clean the barrel.
If you lube the pellets you will not need to clean the barrel as long as the gun is used every week.
Wash the pellets as the crap that is on them is there to stop oxidants forming on the lead .
When washed relube them with good lube I use petroleum jelly as its more a grease than a oil.
Once you have run the barrel in with the lubed pellets you should find you will not need to clean out the barrel till you switch pellet but always lube the pellets .
BY running in the barrel I mean the lube is in the full length of the barrel which you will strip out by using pellets with out the lube you pick.