Suggestions (perhaps just over $100) would be the Gransfors Bruks Small Forest Axe or Wildlife Hatchet. Both are small enough and light enough to carry on a typical camping load out.
I strongly prefer the 6 over the 5. The 5 is just too heavy for long carry. Sure, the increased thickness and fire spindle notch could come in handy if you are in an escape/evade/get home scenario. Perhaps it would be better if kept in a stationary/backup location like a cache or car. But to...
Drop point, plain blade (not serrated), full flat grind. As long as an edge is sharp, I generally see no need for serrations, plus they are difficult to sharpen for us non-experts.
My choice is the Leatherman Wave in black oxide coating with molle sheath, bit set, and bit extender. This setup is reliable, has a variety of attachment options, and meets all the standard needs one might have.
I second the Spyderco Sharpmaker. It is easy to use and creates a scary sharp edge. Make sure you pick up the diamond rods for dull edges and the super fine ceramic rods (and perhaps a good strop - knives plus being my favorite - to get hair splitting results.
Personally, I really like my Eskabar. A little large for a neck knife if you ask me, but perfect for EDC. Make sure you get a Kydex sheath though, the included plastic sheath contains too much glass and dulls the edge with use.
If not a Esee 3 or 4, try any smaller Esee like an Izula/Izula 2 or a Candiru. Also could try a DPX HEST...Rowen is manufacturing the new ones...they're great and small enough to EDC.