You didn't say if your 500 is new or used. If it's new, I agree with Ghmann -- I'd break it down and clean it: blow out the action, trigger area, and tube magazine with air (canned or compressor), give a quick shot of Ballistol to all moving parts (only exception...I wouldn't shoot any oil up the magazine) and wipe off any excess. Then a patch of Hoppe's #9 cleaner or CLP up the barrel, wait 5, one dry patch, and your good to go to the range or start hunting.
Pretty much the same routine after each range session or hunting trip, though you may need to repeat the wet & dry patch a couple more times, depending on how much you shot. Likely don't have to repeat the Ballistol on the action too often...don't over-oil it.
As to bore-snakes, some guys hate 'em...me, I love 'em. They don't do a thorough cleaning job, but they are a god-send in the field, or when you just don't have a chance to do a complete cleaning. My bird-hunts may last for 10 days or more, and I don't do a deep-cleaning in camp. Every evening, I run a bore-snake with a little oil on it through the barrel just to give it a quick clean and keep any condensation from staying in the barrel. Also, I hunt in all kinds of weather, so I carry a lightly oiled piece of Tshirt and that oily bore snake, just to give the barrel a quick cleaning and oiling and give the gun a quick rub-down, to dry it and wipe off finger-prints before it goes in the case. Instead of a an oily rag, a lot of my friends swear by the silicone impregnated cloths. I'm old-school, I like oil.
If you bought a used gun, there may be extensive lead fouling. Lead is pretty much inert, and I have never had much luck removing heavy leading with any chemical cleaners, not without a lot of elbow grease with a bronze-brush. I guess the electonic bore cleaners (e.g., Outers Foul Out), used with a bore-full of chemicals, do remove lead, though it will run you well over $100, and if the barrel is REALLY leaded up, it may take multiple sessions. The only simple way I've found to remove heavy leading from a shotgun barrel is to find a 36-inch chunk of dowel-rod that is about 3/16 inch smaller than your bore, cut a piece off a 100% pure copper scrubber (like Chore Boy or Libby's), wrap it around the dowel, and drive the copper-wrapped dowel up the barrel with a hammer. Sounds goofy, but it won't hurt your barrel, and if the barrel is really fouled, you won't believe how much lead comes out the end of that bore. I bought a well-used Winchester 24 side-by-side back in '64...1st owner had NEVER cleaned it. I could have filled a shot-shell with the lead I got out of it.
If your action is really dirty, or has a lot of hardened grease, you might want to try a long blast of Birchwood Casey Gun Scrubber (NOT Bore Scrubber, which is much more aggressive). Gun Scrrubber is just a blast of rapidly evaporating solvent...it's nasty stuff. You want to wear wrap-around eye protection and use it outdoors if possible, but it definitely will clean out a filthy action...and will also melt the stock finish and dry out the wood and melt plastic or turn it "milky"...be really careful where you aim it.
If you want to use a heavier oil than Ballistol on the parts of the action that rub, you might want to try one of the Super Lube products (oil and/or multipurpose grease) with PTFE. The grease stays where you put it forever, and won't harden with age. It is a fantastic lubricant, I've used it for 20 years on my folding knife collection, on small equipment and guns and fishing reels...it has never let me down. The Super Lube oil is obviously a lot thinner, but still has a tendency to stay where you put it without running. For any long-term storage, I don't think you can find anything better than Super Lube (although I realize I'm butting heads with proponents of Slip2000 and Frog Lube). You can find "sportsman kits" of Super Lube oil, grease and a few plastic paddles, but you'll spend about $12, and get maybe half an ounce of grease and 7 cc (0.25 oz) of oil. On Amazon, you can get a 3-oz tube of grease and a 4-oz bottle of oil (separate, not a kit) for less than $10, and that should last you for years. I buy the grease in 14-oz tubs...but that's 'cause I'm queer for the stuff, and use it on a lot more than guns.
Good luck with your 500. It's a good model.