How to choose laser goggles for low-power laser of specific wavelength?

If the color of the lens is the same as the color of the laser, it's not going to protect you.

Your local regulations or university may set a specific standard, but a general rule of thumb is that for visible wavelengths like this, you would like the attenuated beam power to be less than 1 mW -- comparable to a handheld laser pointer. At that power you don't want to stare into the beam, but an accidental glance won't cause lasting damage. The attenuation of laser safety glasses is measured in optical densities. If you want to knock your beam down below 1 mW you need anything above 0.7 or so. If you want to be able to see the beam with the glasses on, you don't want to make it too high.

Many places that sell laser goggles publish a chart which shows what the optical density is as a function of wavelength. You should consult it to make sure before buying any, but chances are that goggles designed for 650 nm will probably also be ok at 678.

First, I think it is important to start off by saying this:

For any question about laser safety always consult with your organization's laser safety officer!

To answer the question about choosing laser safety eyewear premised off the color of the lens - this is not the correct way to shop for laser safety products. Instead, looking for a pair of laser safety glasses that protect from the wavelength (or range of wavelengths in question) is best (as well as determining the optical density needed given your laser/situation - this can be the tricky part).

I thought this article on common laser safety industry notation for reading optical density would be helpful.

Often times, the laser may come with instructions as to what type of protection is needed to comply with laser safety standards. It is always best to be safe and ask your lab's laser safety officer (LSO) to be certain.