There exists a wide variety of lasers covering the spectral range from the far- infrared to ultraviolet. In the infrared, the Carbon Dioxide (CO2) laser operating wavelength of 10.6 µm seems a particularly desirable one because of the high operating efficiency of such lasers and their spectral purity. On the receiver side we are not restricted to CO2 lasers, and for space-deployed purposes it would be preferable to use semiconductor lasers.
In the visible region, there is a large wide choice of wavelengths and suitable lasers. It is not presently clear whether there is a "magic" wavelength or frequency that would be favored by alien transmitters. The fact that the quantum efficiencies of terrestrial photodetectors drop of drastically in the blue region of the spectrum suggests that we concentrate our "search" in the green to red region of the spectrum. On the receiver side, Dye lasers may be highly favored for their wide tuning range. It is not necessary that the local oscillator laser should be of the same type as that used for the transmitter - this would be unnecessarily restrictive when only a few tens to hundreds of milliwatts are required for the local oscillator. If one wanted to deploy a wide optical bandwidth heterodyne receiver in space, a Dye laser would be a very good candidate. Otherwise we would require many different types of laser to cover most of the visible spectrum.
In order to put out very high mean optical powers, we should consider that the laser transmitter is likely to be solar or nuclear pumped. The laser oscillator itself might not be of very high power - a high power quantum amplifier or a series of quantum amplifiers may be used instead.
Chemical lasers can put out a lot of power and Hexafluoride-type lasers would have considerable potential in this area. Solid state Nd:YAG lasers have reasonable efficiencies, spectral characteristics and beam shape, 1.06 µm or its 530 nm would be a reasonable operational wavelength.
The ease by which it is possible to frequency-modulate lasers might indicate a preference for frequency modulation, particularly if high EIRP's and bandwidths can be sustained over hundreds of light years. If quantum amplifier systems are employed with low-power laser oscillators, it is relatively simple to get a small low-power inter-cavity phase modulator to frequency-modulate the transmitted beam.