Usually, focus-and-recompose is the better first option. It works well in most situations, especially if you stop down a bit to gain more depth of field. If your camera lets you manually choose AF points, select the point closest to your subject to reduce the need to recompose.

Focus-and-recompose can become inaccurate at very wide apertures or very close distances, where recomposing can shift the subject out of the plane of focus. This is most noticeable in macro or other shallow-depth-of-field work.

Manual focus gives you full control, but on many modern cameras the viewfinder focusing screen is optimized for brightness, not precise manual focusing. That means autofocus may actually be more accurate than focusing by eye through the finder. For the best manual-focus accuracy, use live view magnification if available, or a focusing screen designed for manual focus.

A useful tip is to separate autofocus from the shutter button (back-button focus), so you can focus once, then recompose without holding a half-press.

So: use AF with an appropriate focus point when possible, use focus-and-recompose for speed, and switch to manual focus when you need critical precision and have time to use live view.