1) the laser wavelength has to match your detector spectral sensitivity, i.e. a CCD silicon detector is ok for ~200nm to ~1000nm but it will not work with an infrared laser like a telecom laser in 1300nm. In HI again, the laser has to be able to expose the photographic emulsion.
2) the coherence length: this has to be longer than the optical path difference in your setup, otherwise you will not see speckle contrast, i.e. your signal will not have any modulation. the coherence length is inversely proportional to the spectral bandwidth of your laser. He-Ne lasers are very good for ESPI, also Nd:YAG, diode lasers are also great.
3) power: if you have a large object you will need lots of power. Rule of thumb: for a 5cm diameter object you can do with a 1mW He-Ne on the cheap. For dynamic high speed ESPI we used the VERDI laser from Coherent, which gives ~5W!. Great for objects ~1/4 square meter.
4) laser stability: if you are doing long exposures, then the laser beam quality (spatial distribution) and power need to be stable.
go for TEM00 to get a gaussian intensity profile in your beam and go for the cheapest that does the job. Beware that even though laser diodes are cheap, you need a laser driver and possibly a temperature controller depending on your experiment (this is linked to power and wavelength stability)
I 'd like to add a little remark to Pablo answer, 2nd statement. Cheap dpss laser might work as well as long the depth of recording scene is less then the coherence length. Such laser usually has two closely located, narrow spectrum lines and thus you'd see periodically changing zone of fringes contrast white examining it with interferometer with moving mirror. And so you may "catch" the coherence zone at any optical path difference, but the depth of the scene you will be able to record will be limited ( usually it is ~ 2mm ).
I think Pablo has given you all the tips, I would only like to add to his third point, the size , shape and surface of your object are very important for the power of laser you might need. for eg. for large area holograms where long exposure times are often required Stable single mode with long coherence length should be ok!!
Right Fabrice, these CNIlaser are really cheap and effective, and they can customize it for you wishes, incl coherent length.... Moreover Viktor you will have less perturbation to mechanical unstability with ESPI.
Various lasers can be used. All depends on type of a problem which you solve. First of all, it is necessary to pay attention for the sizes and optical properties of the studied object. It is desirable to provide the laser's coherence length larger (at least two times) than longitudinal sizes of the studied area. If you possess the limited possibilities in acquisition of expensive lasers, you can successfully work with the single mode He-Ne laser (633 nm) with ouput power about 40-50 mW. Such laser is rather cheap and can be bought even in Ukraine.
To repeat the terms you used in your question, for ESPI application we should use the lasers which are suitable for HI . In both techniques you basically have the same laser coherence requirements.
If you want to do very fast interferometry, you have to check the light intensity available from the laser with the sensitivity of the camera used.
One thing more, which I forgot with my first answer:
With high-power lasers (usually from a few hundred mW up) and high rate cameras (ans small sensitivity) which usually require a rather large exposure, you also have to be careful in case you study very small objects (a few mm for example) - especially if the object beam has a very small divergence. The concentrated laser beam may heat or even destroy the objects under study.