Supersymmetry (SUSY) is a theoretically attractive scenario for physics beyond the Standard Model which provides a suitable Dark Matter candidate in case R-parity is conserved. If SUSY is realized at the TeV scale, as favored by several arguments, it will be accessible at the Large Hadron Collider (LHC) at CERN within the first few years of data taking. We present search strategies for generic SUSY models with R-parity conservation with the ATLAS detector at the LHC. These inclusive search strategies are based on signatures including missing transverse momentum from undetected neutralinos, multiple jets and leptons or b and tau jets. We show the corresponding discovery reach for the first fb-1 of ATLAS data and discuss possible measurements needed to extract the masses of SUSY particles including the undetected neutralino.