This is just my opinion,others may have a different preferrence Im sure..
Give up buying a kit for you home cleaning and buy individual components.I would buy a coated Dewey rod,a Dewey chamber AR15 cleaning kit and Dewey brushes.As a note the Dewey AR chamber rod can also be used as a pistol cleaing rod.
I like the ProShot bulk patches.They are double knapped cotton flannel and priced right.
Keep the bore snake for field cleaning.Otis also makes an excellent buttstock cleaning kit for the field.
The Hoppe's #9 is a verygood powder solvent as well as a mild copper solvent.I like to use it as it seems to keep copper fouling at a minimum.
Save the Hoppe's oil for hand tools or whatever around the house type applications.It just does not hold up well enough in the AR IMHO.
I would use something like Break Free CLP or Firepower FP-10 CLP.If you want a dedicated lubricant preservative,look at Break Free LP or one of my all time favorites Mil-comm TW-25B which I think is one of the best available.
New firearms...I always field strip,clean and lube everything before shooting.My experience has been that most firearms from the factory are either dry or coated with some sort of funky grease or oil.Some even have bits of metal in the mix from assembly.My last AR had small shavings of metal in the bore.
My routine is to clean the entire weapon everytime it is used regardless of how many rounds have been fired.I was raised that way so Im stuck with the habit.I cant sleep if I do not.Old saying "the sun never sets on a dirty weapon" rolls around in my head.Im so anal about it I have to clean or at least wipe the firearms down before I do anything else.Like someone said here before,"weapon comes first,everything else follows."
HTH