The acceleration of proton beams during the interaction of an ultra short and ultra intense laser pulse with matter is possibly the most important application of compact laser systems with multi-terawatt and petawatt power. High quality beams with a small energy spread are required for applications where spatially accurate energy deposition is important. For some specific applications the target may be located far from the acceleration region, in which case space charge effects and the interaction with an ambient plasma may deteriorate the beam quality during its propagation.Here, first we review a recently proposed method for producing high quality proton beams using short laser pulses and a target made of a layer of heavy ions followed by a thin proton layer with a transverse size smaller than the pulse waist. Subsequently, we investigate the effects of the beam propagation through a plasma slab in a simplified one-dimensional model.