The other popular saw type is the folding saw. If I were to buy a folder, I'd probably get the Trailblazer Products Sawvivor as it has a rectangular frame. I've used triangle frame saws and they're frustrating. Almost 1/3 of the blade is unusable because of the acute angle where the frame meets the blade at the front end. One of the most popular of these is the Sven saw.
When it comes to splitting wood for fires, shelters, etc. the first tool that comes to mind is the hachet or axe. The down side to an axe is that it requires considerable skill to properly and SAFELY use one. Accurate accident statistics are hard to come by, but it is well known that there are many injuries due to improper, poorly skilled use of axes and hachets.
My father's childhood included chopping firewood as part of his everyday chores. He is very good at it and can split firewood with just about any size axe or hachet. I did not aquire this skill as opportunity to learn only presented itself a few times in any year as I was growing up. Because of this, I border on being a danger to myself (and others) when I try to split firewood when out camping. Doug Ritter, on his Equipped to Survive web site, does NOT include a hachet as part of any of his recommended survival kits. He sites the danger factor caused by an inexperienced user as well as the stress present in any survival situation affecting even the experienced user.
I have what I believe to be the safest solution to this problem for the inexperienced user. Instead of a hachet, get what is commonly known as a froe and a dead blow hammer. A froe is used in many disciplines for splitting wood and similar materials. Google "make a bamboo fly rod" and you'll find many references to using a froe for splitting the bamboo.
I have two froes, a 4" and an 8". The shorter one is the Hacking Knife made by Footprint Tools in Sheffield, England. They market it as a tool to remove old glazing compound. I bought it from Duluth Trading in Wisconsin. Look under Cutting Tools. It's good for small logs up to a couple inches diameter.
My long froe is a "Japanese bamboo knife" from the same vendor. It's good for splitting sticks off of about 6" wood.
I've found the same tool in the Garrett Wade catalog as well. Theirs has a coated handle where mine is cord-wrapped.
Both are rated to be hit on the spine with a hammer. I bought a one pound dead blow hammer for use with these splitting tools. The three tools together weigh about the same as a fairly good hand axe and cost about the same as well. You could save cost and weight by skipping the hammer and using a billet of wood or a rock once you arrive at camp.