I know this subject has been beat to death on this thread and on the forum, but here's my 2 cents as a guy would did it the "Army way" till I got out and found my own solutions.
Hands down, the best-quality rods I've even found (after buying MANY sets of many different brands of rods
) is Pro Shot. Between their rods, brushes, jags, punches, and other cleaning gear, they make quality, lasting stuff. I don't like their solvents/oil, but I do like their rods and gear -they'll last for life.
For the solvent, I use M-Pro 7 or Hoppes Elite gun cleaner -they're the same thing, buy whatever's cheapest.
For the oil, I use M-Pro 7 LPX oil, or if I'm feeling like it, Winchester 44 -it's the closest thing I've ever found outside the military that replicates actual military CLP the best -it's not like that knock-off Safariland breakfree stuff (which is a good product, but it's NOT CLP and I hate that they advertise it like that).
I'm assuming you're cleaning a chrome-lined barrel, so with that said, keep in mind that a very detailed bore cleaning will not be necessary for most philosophies of use, but this will work well:
1) Check to make sure it's unloaded.
2) Pop the upper, take out the BCG and charging handle.
3) Use the brush head soaked in solvent and scrub up and down several times in the barrel (going from the chamber to the muzzle -NEVER insert rods from the muzzle into the chamber unless the gun design won't allow you to do it any other way).
4) Pull out the rod, clean the rod and the brush. Use the jag to punch the
right sized patch through the barrel.
5) Repeat this process till the patches start coming out clean. For best results, do a pass with the brush and solvent, then let the solvent soak for a little while, then come back and continue the process.
6) Use the loop head and slide a patch into it, soaking the patch with oil on both ends and send it through the barrel twice, ensuring the barrel gets a very minor coating of oil on the inside.
That will work for any chrome-lined barrel. For heavy-duty accuracy guns without chrome-lining, the process will be a little different.