Download AN1490 Ten Things to Consider When Selecting Your Next Oscilloscope from Agilent Technologies (2009, 14 pages, 634 KB pdf file)
The selection criteria that are covered are bandwidth, number of channels, sample rate, memory depth, display capabilities, triggering capabilities, probes, connectivity, application software and finally your own evaluation of the scope during a demo. Each topic is shortly explained on one page (for further information, XYZs of Oscilloscopes is a good source), so this app note will not make you an expert, but at least you will know which questions you have to ask. It assumes that you have already decided towards a digital scope, specifics of analog scopes are not covered (you can find a good discussion of analog scopes in the Oscilloscope Applications Guidebook by BK Precision).
You may also be interested in some other Recommendations for Introductions to Oscilloscopes.
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