Moderately experienced backpacker here offering my 2 cents.
You're almost certain to have a better time biking around the US than walking. Sure you need to budget for a touring bike, but you can get a Long Haul Trucker and all the gear, panniers, etc., for well under $1500, and then you have no transit expenses except occasional maintenance and repairs - and repairs should not be a major issue because LHTs (or any other serious touring bike) if set up right, are built to last.
If you're sure you want to walk, well for chrissake make sure you have a scenic route for much of the way. You absolutely don't want to be walking along roads the whole way. Check into 4x4 networks, I've heard mountain bikers can cross the entire country on dirt paths, fire roads and the like.
Take GPS.
Make sure you know plenty about backpacking, back country first aid, camping, bear-bagging, navigation, etc. There's some real remote areas out there. Also get good at stealth camping but it's still better to ask someone if you can sleep on their property.
Your gear list looks reasonable for a long backpacking trip. I don't see anything unneccessary on there. Although get a headlamp instead of a flashlight - it's one of the best buys you'll ever make. Batteries aren't hard to find either.
DO NOT GO CHEAP ON GEAR. Money spent on good gear is money well spent; money spent on cheap gear is a waste. It'll fall apart just when you can't afford it to. Good stuff will last half your lifetime or more. Make sure your backpack fits you and is comfortable carrying heavy loads, and make sure your boots are broken in and comfortable. For both of those, do other shorter hikes first to make sure the stuff works for you. Also get in shape first - there will be times when you're carrying like five days worth of food and possibly more than a day's worth of water on your back and believe you me, that is no joke. Water in particular is HEAVY.
Think about saving up and investing in gear that's ultralight as well as being high-quality. REI is a good place to get gear; army surplus is OK but I don't think you're gonna find anything ultralight there, and the quality can also vary, as does the knowledge of the staff. Ultralight options for camping include just a tarp or a tarp tent that you support with hiking poles (which you're assumed to be taking anyway). You can also look into camping hammocks. I have the Grand Trunk Ultralight Skeeter Beeter and love it - it packs up very compact, weighs a pound and 4 ounces, and is WAY more comfortable than sleeping on the ground - and cost like 70 bucks new including shipping. It includes a bug net, hence the "skeeter beeter."
http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs615.snc4/59534_1613253657566_1423039006_31623368_6248452_n.jpg see a picture of it here. The only downside? If there's no trees, you're out on your ass. However, you generally want to take a sleeping mat along to use as insulation in the hammock, so if you can't find trees just sleep on the ground with the mat. You should also have a tarp (shouldn't weigh more than about a pound) in case of rain.
The skeeter beeter can also be flipped with the bug-net side down to use as a spot for a nap, or just to relax and read a book. Hammock camping is seriously the shit.
http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs563.ash2/148573_1721196036058_1423039006_31834084_7192165_n.jpgFor your sleeping bag, think about down versus synthetic. Synthetic is cheaper, heavier and bulkier, and will keep you warm even when it gets wet. Down is lighter, smaller, warmer per amount of weight, pretty expensive, and useless when wet. If you're smart about it, you can go with down and just make sure it always stays dry, and be fine. But be careful with it. And make sure you have a warm enough bag for whatever temperatures you might possibly encounter.
Get a camping stove. The MSR Whisperlite Internationale will set you back like 80 bucks new, plus 20 for a large fuel canister. Or, I got one used on ebay for 60 bucks not including the canister. The stove can burn literally any kind of fuel, you can fill it up at a gas station for a few bucks and have enough fuel to cook for a week. Then get a small light cooking pot and you can cook yourself up all kinds of noodles, rice, couscous, soup, whatever you want.
Obviously you should be able to camp out, but look into Couchsurfing.com. Good way to meet people and have a warm bed and shower to look forward to from time to time.
Don't take a gun.
Clothes, get the lightest stuff you can and not too many of anything, but just make sure you always have something dry to change into. Get a bunch of pairs of wool socks to wear under your hiking boots. Also, Chacos might be a good option, but make sure you like them first; some people love them, some people hate them. Have at least one "presentable" outfit to wear just for when a little bit of extra class helps you make a good first impression. Have layers as opposed to heavy clothes. Have a rain layer and a warmth layer and a windbreaking layer. Have sunglasses and a hat.
I see somebody posting not to take toilet paper. HORRIBLE IDEA. HAVE AT LEAST 3/4 OF A ROLL ON YOU AT ALL TIMES. ALWAYS. I can't emphasize enough how much you don't want to be stuck somewhere without TP when you really need it. TAKE TOILET PAPER. Also a trowel to dig holes, of course. The TP weighs nothing and you will regret not having, in a way I shouldn't have to describe. TAKE TOILET PAPER.
Deserts are not a good place to walk. Hiking across them requires either having someone supply you with water, or else caching it yourself ahead of time. Hiking in the desert without knowing where your next water is coming from is a good way to get dehydrated and getting dehydrated is an excellent way to die. Unless you can find a route where towns are definitely no more than 20 miles apart, I'd tweak your route to stay away from any deserts, or hitchhike/bus through more isolated sections.
Basically, the most important thing is have experience. You have years before you're planning to do this, so use that time doing shorter hikes, getting used to walking and learning the ins and outs. Go on the internet to learn things, meet other backpackers, become an expert backpacker. This is a quite doable trip, but only if you know exactly what you're getting into.
