Sounds like a summer to remember. I did something similar in Alaska 25 years ago-and spent much of my youth camping around Leadville where I grew up. In terms of a stove-Coleman fuel (white gas) is more economical than the little green bottles of propane. If you have a big white refillable barbecue grill propane tank, that's acceptable-though a little more expensive than white gas, and you've got that monster to look at and lug around. Cooking and boiling water to wash dishes with the little green bottles will cost 10 bucks every day or two. A gallon of 10 dollar coleman fuel will last a couple weeks. You can use unleaded from the gas station, but it will clog your generator (the little brass tube that vaporizes the gas in the stove or lantern.) Propane is easier to run, but white gas is not hard to learn, and is so much cheaper if you're running it all summer.
Baby wipes are your friend. Keep a clean camp. Bury your poop a foot deep. Burn your toilet paper. Solar shower makes life nicer. Don't wash clothes/dishes in the creek. Low impact camping. Use established fire rings. Don't go crazy with campfires. Watch for fire bans-you don't want to burn the place down. Biodegradable soap.
Officially, the forest service doesn't want you camping in any single national forest for more than 14 days. I've never heard of anyone getting busted unless they stayed in one campsite for 2 months. Move around, keep your nose clean and you should be fine. Beware of private property. You don't want to camp on some crazy hillbilly's place. The forest service office will sell you a map that kind of shows the limits of private property, etc. There are such offices in Dillon, Idaho Springs, Minturn, Leadville, Glenwood, Gunnison, Salida, Canon City, and I imagine Montrose and Durango. Maybe Alamosa. YOu can probably get them online too. The National Forests are delineated by drainage. Arkansas River (Leadville/Salida)is San Isabel, Upper Colorado (Dillon)is Arapahoe and (Meeker/Glenwood) is White River, Gunnison is Gunnison. Rio Grande (Alamosa,etc)is Rio Grande. Uncompaghre (Ouray area) is Uncompaghre and San Juan (Durango/Silverton)is San Juan. That's how the forests are administered, and in some ways they are little fiefdoms.
I've never had any trouble with bears. They are more prevalent in the 6000-8000 foot area than the 10-12K I'm more used to. Food in your car. Don't sleep in the clothes you cook in. Yellowstone and Montana are a different story, but in Colorado, bear problems are rare.
Don't bring a gun unless you plan on potentially killing someone. Seriously-I've been camping in Colorado for 40 plus years-hundreds if not a thousand nights- and never had the need for a gun on a non-hunting trip. Like the song says, it can get you into trouble, but it can't get you out. It's more risky in the Walmart Parking lot in Denver buying supplies than in any of the places you plan to visit in the mountains.
Fishing pole and license will make your hikes a lot more fun. If you're in the Leadville area-there are a bunch of high lakes above Turquoise lake that are really bitchin little hikes. Nothing better than fresh trout. St. Kevin, Bear, Galena, Timberline, Windsor, Native Lake, Three Lakes, etc. A bunch more a half hour north toward Vail in the Homestake Drainage. A few off Independence Pass-Blue, Lost Man. Each of these is a wonderful day hike. Check in with your family every few days. Tell them where you are going. If you don't check in, they'll know where to send the Sheriff. Be very careful if you're by yourself-a broken leg can be a death sentence if you're in a bad place. In the last month, three people have been found dead a week or two after their families reported them missing. In one case, no one knew where to look until people noticed the abandoned car at the trailhead.
The lakes are frozen until early July up high. Fourteeners too, are pretty snowy through July. Be careful. Don't be afraid to turn back. Read fourteener books-Gerry Roach's is good, Dawson is not bad-2 volumes-Bourneman and Lampert is OK too. Colorado Mountain Club has a book that discusses other peaks besides fourteeners-but it's not as detailed as the others.
Good luck. I may see you in Leadville metro area. I frequently go to all these places I list. I'm the 50 year old with a jealous smile.