Escape315, Welcome to Bladeforums!
I concur with the recommendations to go with a fixed-blade knife, as opposed to a folder. While there are sturdy folders on the market, they are NOT cheap. Very economical fixed-blade knives OTOH are easily found.
Cold Steel Bushman or Mini-Bushman are $15 and $11 respectively at the link below. I recommend the larger 7-inch bladed Bushman.
http://www.wholesalehunter.com/product/coldstee/colddes/bushman.htm
They are one-piece rolled-handle construction with no joint between the blade and handle. While I think the Mora knives are much better pure cutters by a bunch, the sturdier CS Bushman will be more forgiving of poor technique due to deteriorated motor skills (easy to do being tired and/or cold getting caught on an unexpected bivouac) or when used to dig/pry. With little imagination, the handle can be used to store emergency goodies like firestarter, Potable-Aqua water purification tablets, Ziploc bag water container, etc.
--------------
Bushman
Weight: 10.1oz
Blade Thickness: 3/32"
Blade Length: 7"
Steel: SK-5 High Carbon
Overall Length: 12 3/4"
--------------
Mini Bushman
Weight: 7.6oz
Blade Thickness: 2.5mm
Blade Length: 4 3/4"
Steel: SK-5 High Carbon
Overall Length: 9 1/8"
--------------
For dirt cheap (and I am dirt cheap!

) try to find a good quality kitchen knife as Bill recommended, but at a thrift store like Salvation Army, Goodwill, Deseret Industries, St Vincent de Paul, etc. for literally a couple dollars. Garage/yard/moving/estate sales are another source for dirt cheap knives. Flea markets and auctions can be good as well.
If money is less of an issue and you simply want a more indestructible knife, there are lots of good choices among the commercial knifemakers. Check out Swamp Rat Knive Works blades (about $65-$150), Becker knives ($45-$70), Busse Combat Knives (check the secondary market for the Busse Basic modified-INFI steel models at about $120-$200 or the regular Combat Grade models in INFI steel at about $100-$1,000+ depending on size & rarity of model), Fehrman Knives ($100-$350).
For customs, have Mr Siegle make you one of his medium-size (about 8" blade) Hoodlum II knives. Super camp knife, super nice guy to deal with!

Use the "search" button at the top of the page to find info/pics of it.
Check out the list of recommendations I made in the link below, in ascending order of price:
http://www.bladeforums.com/forums/showthread.php?s=&threadid=247653
(edited to add) Saws: If your "secret area" demands working wood that is thick enough to need chopping beyond the CS Bushman's abilities (and it is NO kind of chopper), rather than going to a heavier chopping knife, consider the light weight combination of the Bushman and a Japanese style folding pruning saw with about a 10" blade on it. The teeth on a Japanese saw are pointing back toward the handle, so your cutting stroke is as you are pulling the saw back toward yourself. This is opposite of traditional European/American handsaws with which your cutting stroke is as you push the saw away from your body.
Be sure to get a pruning saw, not a regular woodworking saw. The shallow gullets (spaces between the teeth) and the tooth geometry of regular woodworking saws make them lousy performers on the often green or punky-surfaced wood you will work with in the forest. Pruning saws OTOH have very deep gullets and coarse teeth that have been specifically designed to handle green wood.
Folding pruning saws with blades in the 7- to 16-inch range can be easily found for about $15-$30 at Home Depot, Lowe's, Wal-Mart, hardware stores, garden shops, etc. Their folding nature makes them super-easy to stick in your pack, or even in a pocket. Most of these pruning saws have large lanyard holes, so it's easy to keep them with you. Corona makes a decent pruning saw that is widely available in that $20 range. Be aware that Corona makes a couple different grades of folding pruning saws. Be sure to get ones with stainless steel blades that have the Japanese "cut on the pull stroke" teeth on them.
I recommend saws with blades in the 10" range as a good compromise between being large enough to handle any wood you will need for outdoors work and ease of carry. The wood you will typically be working will be 4" and under. You are not building a log cabin so won't need large logs and, as Cliff Stamp points out, handling long larger logs on uneven terrain is awkward and difficult. That large a log isn't needed for making shelters.
My favorite folding pruning saw is from Tashiro Hardware for about $30. While it is more expensive, it offers the valuable ability to adjust the blade-to-handle angle. Some of the comments in the links below explain why this is important.
http://www.bladeforums.com/forums/showthread.php?t=195322
http://www.bladeforums.com/forums/showthread.php?t=249653
http://www.bladeforums.com/forums/showthread.php?t=268425
http://www.bladeforums.com/forums/showthread.php?t=118353