||In ArcMap, when the data frame is set to a geographic coordinate system (lat/lon), the measure tool will return the geodesic distance. That is, the shortest distance on the surface of the ellipsoid/spheroid.
If you measure the perimeter or area of a feature (using a tool, or with the measure tool for areas), it will use 2D Cartesian math, so this is not that accurate.
Particularly with areas, you should project the data to a projected coordinate system that's using an equal area projection like Albers or Lambert azimuthal.
Buffers are even more fun. The Buffer Tool is also using 2D Cartesian math, so you should definitely project it first if you go that route.
There's also a Project Wizard that you can add back into ArcMap. See:
You can change how it calculates the buffer. Normally, it fits an oblique Mercator projection to the features, but you can change it to use the data's coordinate system, the map's, or calculate a custom projection for each feature. See: