"One side tells me to be aware of all my actions ( Breath, Stepping, Thinking )"
The above is satipatthana / vipassana / sama-sati ("right mindfulness" in the Noble Eightfold Path) practice.
Then I see another type where basically you remove all Mindfullness like entering a void, Blankness and without thought but yet still sort of There.
Two things about the above remark:
- I suspect you may have heard or read about someone trying to describe samatha, but just to be perfectly clear, in samatha -- actually in any of Buddha's instructions I know of -- there should not be a lack of "mindfulness" (sati, presence, awareness).
- The term "mindfulness" above could have been used to refer to satipatthana which is popularly known as "mindfulness meditation".
Satipatthana and samatha present distinct practices, and the Buddha taught both. Though one does not do both simultaneously -- they are known to get in the way of each other -- they may be practiced in conjunction. So, "remove all mindfullness [...]" meaning "not doing satipatthana to do samatha" could start to make more sense, as the descriptions of mental states above suggests an attempt of describing jhanas, which is an array of special "states of mind" often referred to as "absorption states", developed through samatha practice.
What is the type a Buddhist should practice? Or the benefit of the two?
First, there are many kinds of meditations preserved by many buddhist traditions as pointed out in this answer.
Having said that, and speaking of only samatha and satipatthana, popular saying is that one either practices both, or just satiphattana -- it has been brought to attention that there is some ground on the sutras for this position.
The benefit of samatha are manyfold, but the prominent characteristics are of calming the mind and sharpening concentration. It's a practice of samadhi, and as such, it has direct correspondence to "right concentration" in the Noble Eightfold Path: samma-samadhi.
Sathipatthana is often considered to be the "actual work" that drives one to the understanding, to directing the mind to reality, to "directly see" (vipassanā). It also has a correspondence with "right mindfulness" (sammā-sati) in the Noble Eightfold Path.