Whichever you use, a high-powered laser is still a high-powered laser. What's worse is the limited eyewear for the 780nm. Yes, you still need protective goggles, but I have yet to find a cheap pair that has a rating of OD3-4 for 780nm.
Most of the diodes I've harvested were closed can, but I have found 2 that were open. That depends on the manufacturer and drive speed.
As far as the blown diode, you probably did feed it too much current. The big issue with any laser diode is current, and not voltage. It simply happens that to provide one with its optimal current, it usually lies in a certain range of voltages. I strongly recommend building a cheap LM317-based table supply. If you can, go to a place like Radio Shack and pick up one of their 25ohm potentiometers, the LM317 chip, and the rest of the components needed to build DDL's driver circuit. The range of resistance you want for most laser diode tests is 30ohms max to 3 ohms min. This will give you a wide range, supporting low power diodes as well as pushing the higher power ones to the limits. If you don't want to put more risk to your higher end diodes, make sure the resistance can't go below 5 ohms. Here's how this breaks down:
Blu-ray LDs and 5mW red LDs want between 25-50mA depending on the diode. If you can, find the appropriate data sheet and take the Iop rating. If not, start at the adjustable supply's lowest current setting (highest resistance). Use an ammeter in series with your laser diode. From the point where the laser truly kicks in and forms a beam, turn up the current no higher than 10mA. This is a well-respected safe zone for operating your lower laser. Pushing it above this will add risk, but may also increase its output power. I don't recommend breaking 250mA for the higher powered 16x DVD burner diodes, or the GB red diodes.
This said, green pump diodes often require more current than you would expect. Some of those green drivers may spell a fast death to a red LD.
For a good heat sink, I recommend getting a low-cost TEC off of eBay. Many people are offering them for under $20. Remember, heat lowers a laser's output and increases its current draw. This is another reason a regulated current supply is a must. For a housing and simple heatsink, the Aixiz modules do well enough that I use them for my DVD-harvested red diodes. I keep the run-time low on them, however, unless I have the module sitting on a TEC.