Years ago when I was on this search myself, I purchased a Brother CXi 6000 used, It was light weight and actually had a decent stitch, was very inexpensive and small. I used it for classes and get togethers. I found a Featherweight a few years later and now use that. Here are my upsides and downsides of both - Both have limited harp areas so not (imho) appropriate for let say a free motion quilting class,
CXi6000 .... cheaper, new, lots of stitches, a "small table" for a flat surface, electronic, light .... but you get what you pay for imho it is made cheaply. I used it for piecing only
Featherweight .... Tried and true, sturdy, easily fixable, great stitch, light weight, small, sturdy fold down flat surface .... but it is straight stitch forward and back only.
My recommendations would depend on what you type of classes you take. If you are quilting and just want to piece blocks when away from your home I would say look for a featherweight If you are interested in buttonholes, zigzag, and other stitches then you need to look elsewhere. And of course, it is all about the $$ - ie what is your budget? There are a lot of good smaller lightweight machines out there (I am sure others will chime in with their thoughts). All the major manufacturers have smaller lightweight machines if you are looking for new, I would also keep an eye out for used machines - you might find one at a dealer that even includes classes and warranty. All my machines (except for my longarm) have been purchased off of Craigslist.
As far as a featherweight - if it runs smoothly and the light, bobbin winder and reverse work you should be good!! They are easily oiled and greased and most sewing machine places will fix them, While I have the original foot peddle for mine - I purchased a new foot control as I could never get the hang of the older style, Parts are easily replaced and available as well as lots of expert folks to help. As with anything, if you are purchasing used, make sure you try it out - bring fabric pieces with you, try all the options (including the bobbin winder) !! Good luck with your search.