What are the important traits of a good popcorn machine for home use?
There are three non-microwave ways to pop popcorn:


an air popper
a plug-in dome popper
a stovetop popper


Each of these makes different popcorn. 



The air popper uses no fat, though if you're going to add melted butter you probably don't care. In fact the absence of fat means salt and other powdered flavours don't stick well. You can't burn the popcorn. My air popper also used to blow unpopped kernels all over the kitchen. We eventually repurposed it as a coffee roaster.



The plug-ins require a plug, you add a little oil, and you need to pay attention or you might burn a few kernels.  I use coconut oil in mine, and add less butter than I used to add to air-popped corn.



The stovetops are apparently terrific if you want to melt a coating (eg caramel corn) onto the popcorn. I haven't used one. 

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ETA:  Two additional options.

If one already has an electric skillet, such as:
 

With a bit of oil and corn it will hold a steady temperature and do the job without a separate space eating devise.  This option takes a little practice to get the temperature that works best for you, and shaking the skillet a couple times while hot is a pain, but this was always my grandparent's preferred popper.

If you do not wish to eliminate the microwave option, several makers produce these:    

These dry pop for those who are concerned with oil.  Or for those of use who prefer, we dry pop it, then dump on the butter after.  This gives the option though of using spices and such after much like an air popper, but in my experience had a higher pop rate that air poppers of packaged microwave popcorn and was much less prone to burning.  They do require little concentraters that are inserted and would each hold up for 4-6 batches though.