I can't say for sure what is causing your rifle to shoot high for the first shot but often a rifle will not shoot to the same POI on the first shot from a cold bore as it will after being fired. It seems that having a light coating of fouling in a bore will "settle" a gun down and make it shoot to POA.
As for how to clean your bore before loading the first shot, this is a ritual that differs from shooter to shooter. Since I oil lightly with Barricade before putting my gun away, it is a simple procedure for me to clean my bore prior to my first shot. I run an alcohol patch (or two) down the bore followed by a dry patch. I then fire a cap to be sure the flash channel is open. Then I am ready to load. If you are one of the folks who like to use a grease in thier bore before putting their gun in the gun safe, you may need to use a more vigorous cleaning method to get all of the grease (or Bore Butter, etc.) out of the bore to make it ready to load. The important thing is to be sure your bore is clean and your flash channel is open. If the method you are using is getting the bore clean and flash channel open and you like doing it that way, then it is correct for you. Everybody has their own way.
Often a rifle will not shoot to the same POI from a clean cold bore as it does from a slightly fouled bore. That is why there are "cold bore" matches. You just have to learn exactly how far off your POI will be with regard to your POA so you can apply the proper "Kentucky windage" on that first shot.