You can and will get lots of disagreement on "breaking in" BUT everyone will agree that the barrel of a new rifle should be cleaned before shooting so as to remove the greases/oils etc that the factory put in the barrel.

As to following shots I do the following:

If the barrel is stainless I fire a few shots then:

Clean out the powder fouling with Hoppes and brush or similar then dry out the Hoppes and then with a patch on the ramrod put Sweets 7.62 into the bore. Leave for about 5 minutes. Dry out the Sweets and the patch will probably have a bluis green colour, then run Hoppes through the bore and then dry out the Hoppes and then shoot again. I might repeat this every 5 shots or so for about 20 shots.

Don't leave Sweets in for too long and don;t shoot the rifle without removing the Sweets.

If the barrel is Chrome Moly I only clean powder fouling out after I have finished shooting, depending on calibre and number of shots. I don't bother cleaning copper fouling out of Chrome Moly barrels as I think it is better left there. Others will disagree. If the calibre is small but has a larger case capacity such as 22/250, 243, 257 Wby etc them I might clean the powder fouling out after 20 shots or so. For big bores with small capacity for the bore size such as 375 H&H, 458 Win I would only clean out the barrel after I finish shooting.

Having said of all that the vital thing is to clean out the factory barrel protection before shooting.

After you have fired 3 or 4 shots tighten the action screws. The front screw shoul be tightened quite hard and the rear screw not tightened up to much.....somewhere between being "nipped up" and very tight.

Mike