Light Weight Axe and Machete

These are items that you should definitely spend extra money on. A light weight axe is better than a hatchet, as you can cut down larger branches and small trees with it much easier than a hatchet.
The machete is important, because there's a great chance that you won't be on any noticeable trail at times, and may have to chop your way through heavy brush. Spend extra money on a good machete. Avoid cheap machetes, as many don't have good handles, which can break apart after repeated use.
(If your hiking pack is too heavy, consider passing on the machete. The axe is more important. Definitely pack that.)

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