You're going to get about 10,00 different answers here.
Stay away from stainless brushes, stick with either nylon or the traditional bronze brushes.
Find a rod that feels good in your hand and is appropriate for the job at hand. They sell rods in all different lengths, diameters, materials, and coatings. If all you are going to be cleaing is a .22 pistol, don't buy a rod for cleaning .45's or for .22 rifles. I prefer one piece rods but there is nothing wrong with multi piece rods, they all get the job done. A coated rod makes sense on paper, but when it comes down to it a brass rod will do just as good of a job. Any concerns about grit or whatever can be addressed by wiping the rod clean from time to time. The brushes that come with the cleaning kits have always seemed to work as well as more expensive ones for me, provided they are the correct size. One thing you should be aware of is that these brushes should be viewed as a consumable item, meaning over time they do wear down and need to be replaced.
There are a million and one solvents, oils, lubes, etc out there and almost as many opinions as to what is the best and what does and doesn't work. Its really a matter of sorting through all the reviews online, deciding what to try and seeing how it works for you. What may work for Joe Blow in Portland, OR may not work so well for Johnny Whatshisname in Miami, FL.