Schooner, welcome to the forum, and congratulations on choosing a fine rifle.
You should give your rifle a good cleaning before shooting it, to make sure there isn't any metal swarf or particles from the machining process. The key thing to remember is you never want to drag or scrape any of your cleaning tools on the edge of the bore at the muzzle (called the "muzzle crown"). If this gets scratched or chipped, it's goodbye to accuracy and re-crowning costs about $50.
My favorite tools for cleaning are:
1. Patchworm pull-through kit. Only handles patches, not brushes, but works very well. I like using it as a quick cleanup when at the range, since it fits in my bag.
2. Stainless-steel or carbon-fiber cleaning rod, such as this one:
http://www.brownells.com/gun-cleani...ng-rods/cleaning-rods-prod57075.aspx?psize=96, or this one
http://www.brownells.com/gun-cleani...s-steel-cleaning-rods-prod35246.aspx?psize=96. One big advantage of the Takedown is that you can always clean from the breech and won't be pushing tools all the way through the muzzle. Yes, these rods are more expensive than the Hoppes or other bargain-priced rods, but they perform that much better, too. A rod that is too flexible will bend in the bore and scrape it as you push a tight patch or brush through. Not good.
I strongly discourage buying a segmented cleaning rod. They are too flexible and the joints have sharp edges that can scratch your barrel. I also don't like coated cleaning rods because grit can get embedded in the coating and get re-introduced to the bore.
3. Brass patch jags, either the pierce type or the Parker-Hale type. Dewey makes good quality jags and brushes in their "No-Harm" line.
4. A good chamber cleaning brush, such as the Brushn'Mop from
http://www.gunsmithertools.com Cleaning the chamber is especially important because our rifles developed a hardened carbon ring in the chamber quite quickly. This ring, if allowed to build up, impedes the round from seating properly in the rifling which can affect the accuracy and reliability of the rifle.
The most authoritative article on .22 rifle cleaning that I have seen so far is this:
http://www.rrdvegas.com/rimfire-cleaning.html. I encourage everyone to read it and consider its recommendations carefully.
I also discourage the Boresnake because it picks up dirt and grit on the first pass and should be washed before going through a barrel again. I keep a clean one in my range bag in case someone needs an aggressive cleaning while on the line. But each time it is used it goes through the laundry again (in a mesh lingerie bag in the washing machine and dryer.)