Mike,
First off, welcome to IAP!
With respect to eye protection, I wear goggles and a face shield while turning. I've had too many larger chunks come flying at me to feel comfortable with anything less. I also use CA for most of my finishes, and the last thing I want is a ball of still-wet CA coming at my eye. Somehow I managed to glue my face shield to my hair one day (without ever getting my hands near my hair), and that just reinforced my eye protection requirement.
As for breathing stuff, that varies. Some woods, such as Cocobolo, Walnut, and spalted woods, are known to cause problems (some in the short term, some longer term), and when turning those I almost always wear some kind of protection with those. I usually wear a disposable mask, but one of the better quality ones you find at HD or another big-box store. I'm thinking of investing in a respirator, though, because I've had some batches of CA that really threw me for a loop, and I think I'd be more comfortable with a respirator and the better quality filtration it typically provides. For the other woods, I may not always wear a respirator while turning, but I typically wear one while sanding and finishing. I'm more concerned about the dust than the shavings, which may be an oversimplification of the risks, but I figure I'm likely to inhale more of the dust than the shavings.
Some here use those powered respirators that clean the air and pump it into a face mask for you. If I sell some more pens, I might consider something like this.
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The mask I use is similar to http://www.websoft-solutions.net/3m_8511_3m8511_3m_dust_respirator_p/8511.htm