Every survival situation will require tools, the oldest and most versatile of tools is the edged weapon or blade. What type of blade/s to have are often a matter of great debate. So here's my thought on the matter.
You should maintain three cutting blades as a minimum, the first being a locking foldable knife which can be operated with a single hand. When closed it should fit mostly inside the closed hand. This blade will serve many purposes, closed it provides a weight and solid backing inside the closed fist for fighting, should the skirmish escalate, it can be quickly opened and used for more painful or permanent defense measures. The blade can be quickly heated to sear wounds to stop bleeding, It will also be a workhorse for trimming and cutting tasks. The second blade should be a form of multi tool, there are many available look good quality. This tool should have common screw driver bits, an aggressive saw, pliers with wire cutters, and an awl punch as a minimum. Mine is more geared towards firearms maintenance. Last is a long blade, by this I mean a serious work horse. Whether you go with a survival type knife, a machete, or a combat axe really to me depends on what your primary needs will be. Inner city would benefit more from a combat axe because there environment will require constant breaching. Almost everything they might need to access will be behind wood, glass or metal. Machetes and survival knives would fall short of meeting this need. The farther away from the city you get the more your needs change, much of what you gather will need to trimmed, cut, or dug. this includes building shelters. Here a machete with a good saw back is invaluable, or like myself I prefer a survival knife and possess a separate folding saw. These are minimum needs most people I know have more than three bladed tools. As always the best advice is get what you are skilled with and comfortable using.