Ditto the advice about a good one piece cleaning rod. I use and recommend Dewey's one piece rods, with the appropriate attachments. You will also want a bore guide--it makes life so much easier!
Other stuff you will need:
A good double ended toothbrush. This will help in cleaning the upper receiver.
Properly sized patches. I use the GI patches available from Brownells. These are made to MIL-Standard, and are the best to use in my experience.
A few chamber brushes. I'd probably spring for the Dewey Chamber cleaning kit, also available from Brownell's. It doesn't cost much, and you have a fixed bronze rod that will do a good job.
While you're at it, get some big patches as well. These will help you sop up oil and solvent from the barrel extension (the place where the bolt itself locks up on the barrel/chamber face).
Pipe cleaners. If you break open the rifle and remove the bolt carrier group, you will see the end of the gas tube. Around the outside of the gas tube where it comes back into the upper receiver group are four holes. These are gas relief ports, and a pipe cleaner with solvent will remove the gunk and grime.
Remember when cleaning to run something down the buffer tube (receiver extension). It can stack u0p some dirt, as well.
Pay attention when you clean to the INSIDE of the bolt carrier where the bolt itself lives, as well as the "tail" of the bolt itself. Carbon loves to bake itself on there--after all, the gas that cycles the rifle comes down into there first, from the gas tube. To prevent a nightmare of cleaning, wipe it off with solvent after every trip to the range.
Finally, a HUGE portion of the problems with the AR family can be cured by keeping the chamber, barrel extension and bore clean, and remembering that the AR rifle loves to be run WET. Use a good oil after cleaning to put a heavy film on the bolt carrier group, and the bolt itself. Don't forget to put a drop on the locking lugs, and to spread it around. A drop on the inside of the charging handle where the carrier key rides won't hurt, and don't forget two drops of oil down the carrier key itself.
Congratulations on your new rifle! If you need any more help, just ask--there are tons of folks here to help.