A couple of other cautions. If you use a copper remover, use only the bore solvent and other cleaners and oils recommended by that brand. Some chemicals don't mix and cause corrosion.
I think Sweets can be used with Hoppes Number 9.
A lot of the benchrest people were using Jim Brobst Bore Paste or similar products which removes the fouling and puts a microfine polish on the bore over time.
If you clean on every shot for the first 10 shots with sweets, you'll start to notice less and less blue gunk coming out. The barrel is picking up less copper fouling.
If it isn't, you can fire lap it with NECO's kit--check the Sinclair catalog or site.
But, having done all this religiously with a dozen or so rifles, the last upper I purchased--a high-rise DPMS bull barrel--I just shot the thing with copper jackets and cleaned it with Hoppes and it will shoot dime sized groups at 100 yds all day.
I've read also the you don't want the barrel TOO smooth, just smooth enough so it won't foul heavily.
I've also been reading some negative things about moly. I've shot moly extensively and although I question that it has any harmful effect, I don't think it helps any either. it's just another chore to do, IMHO. So I'm eventually going back to copper.
Remember too that most guns suffer more damage from over-zealous cleaning (military-style) than any other cause. You don't *have* to scrub the inside crevices of that bolt carrier free of all carbon, for instance, or take apart your M1A--which screws it up.
The service is like Catholic School. They really get to you. I've been out 20 years now, and I still get the remorseful crawlies if I don't clean every itsy bitsy little piece, or heaven forbid, leave it dirty in the gunsafe.