Just make sure they go around the side of your eyes too, for when you tilt your head, just try not to do this if you can help it. Specially around metal chips and the tables without cleaning it first, just in case you really have to. There are others that go around the side of your head and look more like regular sun glasses, I just didn't thing they had enough to cover my eyes though. I think the first one will be the one before you go to the goggles if you really want to cover all of your eyes, but just try to stay calm at all times when working on a lathe or any machinery and take the proper precautions and you should be fine. Since your work space is very small, I would also suggest a wet/dry small shop vac to keep the area clean from chips. I hate blowing chips all over the place and this helps me keep things clean and neat. I probably turn it more often that I should, but hey, that's how I like it. Also, the first link for this glasses works great if you have to get under your car. I had the smaller type, and well, got dirt in my eyes, so I went to these and they are somewhat comfortable to keep on too.
http://grizzly.com/products/VOLCAN-S...k-Clear/T20449
Here's the other page with all the different type of safety glasses. By the way, kudos to you, asking for the safety equipment before doing anything is the smartest thing any of us can do. So we know you got the common sense.
http://grizzly.com/products/searchre...aspx?q=glasses
If glasses bother you, there are also full face masks that you wear over your face and you put them on like a hat.
http://grizzly.com/products/searchre...=face%20shield
You can find safety glasses at most hardware stores or even some auto parts stores, depending on where you live and what's available. This stuff is available pretty much anywhere. I can't think of any one that doesn't want to safeguard their eyes or any other body part for that matter.