what should be the correct intention while doing good deeds and acts of worship? if it is only done in greed of receiving the rewards of paradise and saving oneself from hellfire and not necessarily done purely for the sake of Allah or to worship or love Him. is this intention valid?

Yes, that intention is valid, and it is the way of the Prophets and the believers. Allah, the Exalted, praised those who call upon Him in hope and fear, saying, the meaning of which is: "And call upon Him in fear and hope; indeed the mercy of Allah is near to the doers of good" (Surat al A'raf, ayah 56). So worshipping Allah while hoping for Paradise and fearing the Hellfire is not a defect in sincerity, because you are seeking His reward and fleeing His punishment, and both of these are from Him. Do not fall into waswas.