The key parameters for the laser are the laser wavelength and the optical output of the laser. Raman is a vibrational spectroscopic technique and you can basically use any laser wavelength to change the vibrational states of the molecules of your sample material. There are, however, several factors that influence your choice of laser wavelength and you will likely have to make some compromises. All materials exhibit Raleigh-scattering which creates a baseline level in your Raman spectrum that can be larger than your Raman signal and thereby make it difficult to detect your Raman signal. Since Rayleigh scattering is proportional to 1/ λ4, you would get the lowest scattering by choosing a long laser wavelength. Unfortunately, many materials exhibit fluorescence at a longer wavelength, and the fluorescence will also create a background level that can mask out your Raman peaks. A further complication with wavelengths above 1100 nm is that you have to use special detectors made from for instance InGaAs which is generally much more expensive than Silicon detectors that can be used up to 1100 nm.
The most popular laser wavelength for Raman is 785 nm because it is a good compromise between scattering and fluorescence for most materials. Also, with 785 nm as your laser wavelength, you can cover up to 3650 cm-1 (1100 nm) of Raman shift and still use a silicon CCD detector. Other common wavelengths used are 532 nm, 830 nm, and 1060 nm.
Your choice of laser power mainly depends on your cost target and the damage threshold of your sample. Obviously, the higher the output power you need the higher the cost of the laser. Also, if your optical power density on the sample becomes too high you may damage or change your sample which is undesirable. As an example, if you are measuring on human skin, for instance, you don’t want to burn the patient.