http://lewisandclarkjournals.unl.edu/ <-- Journal of the Lewis and Clark expedition. This is my contribution to the thread, as I am under 21 and have not spent much time in the woods outside of some very basic stuff. This is how I would approach the problem.
I would start in Savannah, Georgia and end in San Francisco, California. San Francisco Bay is a massive, easily recognized terrain feature. I must simply reach the west coast and walk in the right direction. The climate in Georgia is far from tropical, but it is warm, and is probably more forgiving of a starting point than somewhere farther north and therefore colder.
I would set the pickup date for 1710. Problems have a way of popping up, and I would want to take it slowly and carefully, as well as spend some time looking around--I mean, this really is a once-in-a-lifetime shot, and I'm not going to rush it. Besides, San Francisco Bay is a beautiful area with plenty of arable land and a native settlement.
I would get a tooth replaced with a radio receiver of some sort, and put a powerful transmitter on the time machine--as I get closer, tooth vibrates harder. No sense missing my pickup because it landed in a tree, and it's not like there will be interference. An added benefit is that I could lose track of time and still make it.
Prep: Getting tattoos, vaccinations for everything, and I mean everything; a cultural study of the major Native American tribes of the period, and as much practice as is reasonable with a primitive bow and an experienced bowhunter/fletcher.
Tattoos:
1) Tattoo of the map of the continental US with rivers, mountains, forests, deserts etc marked clearly with as much detail as possible on my back. Tattoos of specific regions such as the Ohio valley, the Oregon trail route through the rockies, definitely California, Georgia, and other important areas along the route, determined by careful evaluation of maps and measurements of available space on my body put everywhere space is available.
2) Face tattoos designed to inspire impressions of native deities; another thing to consult historians about.
Weapons: Snares, Machete (sharpening stone),
metal arrowheads as many as reasonable, modern arrow-shafts and feathers, and compound bow. 20lbs C4 + detonators. Several small spray bottles of aerosolized smallpox
Kit: Pot that doubles as hat (with strap, handle and visor!), cap and piping to allow conversion for use as a still. Compass-watch, small enough to swallow if required, as well as multiple backups. An altimeter on that watch would probably be nice. Modern pack, Several bladders for carrying water, modern waterproof, insulated blanket, cute fuzzy stuffed animal, preferably built to last, oh and a poncho.
Clothes: 2x durable pants, warm, long sleeved shirts, moccasins
Consumables: Two durable bottles of grain alcohol. One month worth of food. One week worth of water. Several cigarette lighters. Several pounds of seeds (no idea what, I'd have to ask a farmer before I left)
Other equipment: a laminated copy of the ranger handbook with important phrases in as many major native languages, information about assorted useful plants, and as much basic chemistry calculus and physics as I can fit in the margins.
Assumptions:
Everything I pack in will be lost, broken, stolen, consumed, or bartered by the time I get to the other end--probably much sooner, therefore, I should start early doing what I will have to do late. Moving in with the natives, learning their ways, moving west with them, and staying put in their encampment during dangerous weather.
I will not encounter many Westerners (Savannah didn't exist in 1700), but will encounter many natives. I must exploit their knowledge of the area, survival skills, and food stores whenever possible. The locals are likely to have better area knowledge, better bushcraft, and better information about possible routes than anything available in the present day, therefore, I will learn from them whenever possible. The French I find will not be a problem, as my French is marginal, and I have a map of the country on my back which I am willing to share.
Strategy:
This can be summed up as 'go native early and stay that way'. Whether or not it's possible to pull it off on foot without 'going native' is up for debate, but I certainly wouldn't try
The pot and machete are obviously awesome--even Johnny Appleseed had a pot-hat.
I imagine that gun, ammo, and cleaning kit will not be adequate for the entire trek, and that anyone who tries it would eventually be using improvised weapons anyway, so no gun for me. I'm surrendering to the inevitable and using a bow from the start, instead of waiting to run out of ammo before trying to learn to bow or spear hunt. My clothes will wear out anyway, so I had better get used to wearing moccasins and native garb sooner rather than later as well. The blanket is a shelter, a sleeping bag, a sail and generally too useful to not have.
Travel will be slow and steady, involving the (hopefully) willing assistance of the locals.
The C4 is for making loud scary noises to drive off animals, put on a show of force for natives, and clear rubble when necessary. The stuffed animal is for company, and for gaining the trust of the kids. The still and grain alcohol are for the natives--they're missing an enzyme after all. The initial food and water should last long enough for me to link up with (friendly) locals in Georgia, study their ways, and prepare a route north, then west along the Oregon trail, and south to San Francisco.
The smallpox is for returning unopened.
Probability of success: Low to moderate
Probability of successfully settling in with a tribe in a nice section of pristine, clean, pre-colonial American wilderness and starting up a family after missing my ride? Not terrible.