OK, keep reading and using the search function.
Others will think I'm nuts, but based on your background, I would start really inexpensive so you can learn what works and what doesn't before spending your money on something sexy and expensive that you may find disappointing.
So, get an LPC-815 and a PHR-803T sled on order. You should be able to get them for less than $13 ea plus shipping to Italy. Each one contains 2 laser diodes and a bunch of optics. You won't be disappointed. You can even use the lens in the sled to focus the beam, if you can figure out how to mount it.
Next get 2 or more Aixiz modules on order for $3.50 ea or less. You don't need them, but you will want them. If you are ordering direct from Aixiz, buy one of their $5 glass lenses too, they are worth it.
Finally, you need access to the following:
- Low wattage soldering iron with a small tip, some solder, and some hookup wire.
- DVM
- Variable voltage power supply good for 0 to 12 v or so and at least 0.5 amp (you can make this yourself using a wall wart, a LM317 w/heatsink, a potentiometer, and a capacitor).
- a couple of 10 watt or better resistors around 30 to 60 ohms.
Whether you want safety goggles depends on how careful and paranoid you are, and whether you understand exactly how eye damage can occur from a laser strike. If you aren't always very careful and/or don't understand, then you need the goggles and you can use the search function here to find threads about that. It is, of course, a good idea to use them in any case.
While you are waiting for your sleds to arrive, learn all you can about them on this forum and by using google to search the web.
When the sleds show up, be careful of electrostatic discharges that might destroy the diodes. Harvest the diodes and hook them up to your power supply in series with the power resistors.
Point the diode at white paper so you aren't looking into the beam. Slowly turn up the voltage and observe the current through the diode, the voltage across it, and how much light you are getting. Be careful not to push the current too high (you found out the liimits already from all your research, right?).
Next, use a magnifying glass or a lens from a sled and focus the beam. Try popping a few baloons, lighting a few matches, burning some electrical tape. Try different colored stuf at different distances. You may need to use black magic marker and focus close to get this to work, depending on the color diode and how hard you push it.
If you want to get an idea of the laser power, you can build a Simple Laser Power Meter
http://www.laserpointerforums.com/forums/YaBB.pl?num=1239209882 or find a real one at your university.
This should keep you busy for a few weeks and give you a good idea of what you are dealing with.