Because I have touchy sinuses, I wear a full face respirator when I air spade or knife. It looks like these:
http://tinyurl.com/am9p3rr
It works great and you don't have to worry about soil and bits getting in your eyes either.
Although I won't work without the respirator, it does tend to get a little heavy after several hours. I've always been tempted to tie a rope from my belt to the back of the mask to hold my head up, because at the end of the day my neck is exhausted.
I don't think a hard hat is really necessary, but wearing a bandanna to prevent soil clods is helpful (of course, I have long hair, which makes a difference).
With the air knife I wear thick leather gloves, because the aluminum barrel gets hotter than blue blazes. But even the couplings on the air knife get incredibly hot.
I've used both tools in shorts and a tshirt, it's not the worst experience ever, just some stinging. I prefer long pants, long sleeve short with a button-able collar.
For people who get ear infections, I recommend using muff style hearing protection.
And everyone should use a Neti pot to rinse out your sinuses when you're done. Even if you wear a respirator.