If you're going to be doing a lot of projects like this, a good starter investment would be an adjustable power supply. You can normally find a cheapo 0-30V 0-5A one for just over $100. With that you could hook the diode up to the PSU and test it out at whatever current or voltage limit you want.
For a very basic circuit to run it you could always use some variant of the LM317 circuit we love here. The current demands of the diode are quite high, so you probably couldn't run it at full power from a 317 and you'd need to make sure you use the TO-3 LM317K with plenty of heatsinking. You could just take an LM317 circuit though and use a higher current regulator like the LM1084 (again with good heatsinking at that high a current). I'm sure there are much better ways of doing it too, but I'm not very experienced with electronics.
A simplistic way of looking at multi-mode in this context is that with a single-mode diode the cavity is so small from top to bottom that only the simplest, cleanest mode can be supported. Whereas when you increase power and cavity size, modes corresponding to more complicated ways of supporting an electric field can exist. There are far more rigorous explanations than that on google if you're interested. From a practical context though, this means your beam properties are going to suck compared to what you could get from a single-mode diode. Its common to see collimated multi-mode diodes have >3 mRads divergence and a beam diameter >3mm, and that's if you're lucky! You have a lot more power than you'd typically get with a single-mode, but its also hard to get that power at high intensity at distance because the beam's so damn big.
For goggles, I don't know how much good 808nm goggles go for now so I dunno if this is a decent price, but I have some new, quality Glendale OD3+ 804-1700nm goggles I could sell for $85+shipping. Keep in mind at 808nm this diode is going to appear very dim despite its high power, so you have to be extra-cautious with safety! (well, at least the light from the diode will be dim. If the diode itself appears dim it may already be too late to save your eyes! =P)
PS: Cool avatar picture, where'd you find it from?