When I take to the woods, the first thing I grab is my axe. A good axe can save your life. When I have a gun in my hands, I opt for a 1lb hatchet instead. As a rule, I always carry on my person, a magnesium fire starter, small sewing kit/fishing kit that includes both needles, monofilament line that serves as both fishing line/sewing thread, a few buttons, safety pins and selection of hooks, flies and spinners. I also carry a small, nylon cased first aid kit within which I also include a roll of braided picture wire for snares. On my belt is my trusty Gerber multi-tool and in the watch pocket of my jeans is a small Case XX folding knife. I usually carry a small backpack that contains a light poncho, dry wool socks in a zip lock bag. Steel mug that'll serve as a kettle in a pinch. I'll usually have a few tea bags & some packets of real sugar in a ziploc as well, although, I can usually make a decent tea from the plants I find if I had to as in a survival situation. Taking the time to educate yourself can really boost your self-confidence.
In the pack I also include a Pr. warm, synthetic gloves ,a ziploc bag of my own trail mix, a roll of flagging tape and a partial roll of duct tape. The latter can be used to fix broken gear or even blisters on the feet, etc...My Silva Ranger Compass resides in my left breast pocket of my hunting shirt and is attached to me via a length of 550 para cord. In fact, all of my important items are secured to my person via 550 para cord. That way, its impossible for you to lose them, even if they fall out of their pouch or pocket.
I'll usually carry an extra BIC butane lighter or two as well. The magnesium fire starter with built in flint makes the BIC redundant, but the latter is generally a little more convenient. When hunting I usually carry a pair of Cobra 3 Watt GMRS radios as well & a small roll of 550 para cord. I've used the latter to help skin out moose when on my own, by staking out the animals legs, tying them to nearby trees or cutting stakes if there is no nearby tree or shrub to use. Great stuff that para cord!
In a survival situation, you can last weeks without food, just as long as you remain hydrated and warm. That means shelter & fire, for both warmth & to boil water.