How do I buy and test an oscilloscope?
Price points always vary - especially with used scopes.  You're likely to find a lot of old Tektronix two-channel analog scopes.  If you're lucky they will include probes.  


Bandwidth - You should look for 50-100MHz.  Bandwidth tends to increase in multiples of 100 after that point, then multiples of 1GHz after the 1GHz mark.  You might find a 150MHz or 200MHz scope on an odd day.  Again, can't really give you a price point, but the knee of the price curve is in the low 100's of MHz.  Beyond that it tends to get pricey.
Features - two channel at least.  If it's analog you basically get no really cool features (like measurements, saving waveforms, etc). It will be only for viewing waveforms and you'll be figuring periods and such by counting tick marks on the lines on the screen.  Once you get into digital scopes the world starts to change a lot.  I typically like digital scopes more and look at least for measurements (evaluate period, Vpp, etc automatically) and cursors (graphically mark points on a graph and evaluate time deltas, voltage deltas, etc).  Other features that are nifty are USB ports to save waveforms to thumb drives, network connectivity, printer connectivity, logic analyzers and many others.  Generally, once you make the jump to digital you see a significant price increase (a few hundred dollars at least) and get many of these features essentially for free.
0-$400 for an analog one (hopefully in working condition) and digital ones can start around upper $100's of dollars and, well, sky's the limit really.  I should mention at this point that you can get a fairly decent digital 50MHz Rigol Oscilloscope for about $500 or so brand spankin new.  It's by no means a Tektronix but it is very serviceable and has many of the nifty features I mentioned above. 
Some people on eBay will say things like 'powers on'.  This means... it turns on.  And potentially nothing else.  True, some people are idiots and don't know a working oscilloscope from the Dalai Lama but I wouldn't count on this.  You'll want to make sure that it both powers on, passes self-test (many digital oscilloscopes have this and will notify the user on startup if the self-test passed) and that the test signal works on all channels.  The test signal is usually a 1KHz square wave or something similar.  It's built in to the scope and there's a contact point for it on the front of the scope.  If each channel can read the signal it means that if there's a problem with the scope it's going to be in something not immediately obvious - like its bandwidth is declining with age, or it powers itself off after 3 hours of use and won't turn on again until it cools down, etc.  


The only other piece of advice I can give you is to watch out for probes not being included.  Generally they will say but even if you see a picture with probes in it don't assume they're included with the scope. Ask.