I've got two recommendations for you depending on where you hunt:
Silky Saws:
Generally recommended as "the best" and they are exceptional. These have thinner blades which might flex more on the push but they cut on the pull stroke anyway. These are by far the KING at cutting evergreens and softer woods. I don't know of anyone that's tried one that has anything bad to say about them.
Corona Saws:
These have a bit thicker blade and are also fantastic. They cut soft woods about 20% slower than a Silky, but cut hardwoods and dried hardwoods about 20% faster. These have a lifetime guarantee and a nice locking mechanism on the pivot point also. Where i hunt, its mostly hardwoods so I stick with a Corona now. The only downside to Corona's are they only come in 7" and 10". I find the 7" to be almost as efficient as the 10" but easier to pack so it's my go-to now. The 7" does bind up when first starting cuts a little more though, but that's a problem that most tiny folders have due to leverage.
Between a Silky and/or Corona, you should be able to find a coarse tooth saw to fit your size, budget, and preferences for wood types. It's hard to go wrong with either really. Oh, and I find curved bladed saws to cut easier than flat, but sometimes they have teeth exposed when folded if that matters to you. The 7" Corona doesn't when folded up but the 10" does have exposed teeth.