In some occasions autofocus doesn't focus what I intend it to. What is the better option - to use autofocus, focus what I want and recompose, or use manual focus in that situation?
In general, modern AF cameras have focusing screens optimized for bright viewing rather than accurate focusing. This means that the AF system is potentially more accurate than your eyes using the focusing screen, if the AF system is calibrated correctly.
I've found that the wider the lens is, the harder it is to achieve critical focus while focusing manually.
For critical manual focusing, either use Live view, if you have it, or install a custom focusing screen for your camera.
If you are using AF and recompose, I've found it useful to decouple the focusing action from the shutter release. Most cameras will let you assign focusing to a separate button, instead of having to maintain a half-press of the shutter while recomposing-
Focus and recompose will work just as well in most cases; the exception is when the aperture is so wide that the object being focused on actually leaves the plane of focus when you recompose (most likely in macro photography). If you are able to select AF points manually, then choose the one that's closest to the item you are focussing on to minimise this effect.
If you have the time and the means (e.g. zooming in on live view), manual focus will give you full control, but if you're in a hurry, stop down a few stops (if you can) and use focus and recompose.
You don't state what camera model you're using but if it somehow happens to be a Hasselblad H4D series then you're in luck as your camera has a truefocus feautre.
This is essentially an orientation sensor so that you can focus and recompose and the camera automatically adjusts the plane of focus to accommodate for the shift when you recompose.
I always lock the auto focus point selection to the center and not auto point selection. That way I can first put the focus where I want and then recompose.