Excellent choice on a first gun, you'll love it. Adding my (mostly redundant) thoughts to Barry's:
Cleaning: The Hoppe's kit you describe sounds perfect. Hoppe's is a respected brand. Don't bother with a bore snake or other fancy crap for now. And follow the manual.
Check: I have nothing to add to what Barry said.
General: You'll definitely want to buy your own eye and ear protection. I wear glasses so I can't advise on eyes. Ear protection is very cheap and very important, pick up a basic pair at your local sporting goods store for maybe $20 in the hunting section.