What qualities should I look for in woods to be used in outdoor furniture and what are some examples of woods which have those qualities?
What finishing options do I have for weatherproofing wooden outdoor furniture?
The main concern for outdoor use is usually exposure to moisture and subsequent rot. Woods that are used outside should either have high decay resistance or be well protected from the elements by chemical or physical means. I'll explain:
Your options for finishing are basically two: paint for opaque, and spar varnish for clear. Spar varnish is more flexible than other clear finishes, allowing it to expand and contract with the wood and the seasons without cracking and flaking. And it has UV inhibitors to prevent degradation.
Outdoor finishes have to be able to stand up to many adverse circumstances, including UV rays, moisture, and insects.
If the finish absolutely has to be long-lasting, marine epoxy finish is the way to go. It is used by boat builders mostly and can be quite expensive.
Cabot makes a product called Australian Timber Oil that I've found works pretty well outdoors, but it requires re-application every so often. Most outdoor finishes require a regular maintenance routine to keep serviceable, so that's not a point against it.
Exterior-grade paint is another option, with a similar maintenance requirements.