First, think about what you will use it for and where.
Where will you use the scope (on the bench, at a customer’s site, under the hood of a car)?
How many signals do you need to measure at once?
What are the maximum and minimum amplitudes of signals that you need to measure?
What is the highest frequency of signal you need to measure?
Are your signals repetitive or single shot?
Do you need to view signals in the frequency domain (spectrum analysis) as well as the time domain?
Bandwidth: You should look to purchase an oscilloscope with a bandwidth five times (5X) higher than the maximum frequency of the signal you need to measure. This ensures an accurate representation of the waveform. Unfortunately, high-bandwidth scopes are expensive, so you may need to compromise here.
Memory depth: Digital oscilloscopes store captured sample points in memory. The amount of memory the scope has determines how long it can store the signal before having to dump it. This can limit the effective sampling rate of the oscilloscope if there is insufficient memory. This is most apparent when zooming in on a signal.
Channels: Two channels let you compare a component’s input to its output. Four analogue channels let you compare more signals and provides more flexibility to combine channels mathematically, while 6 or 8 channels allows for either multiple bus analysis whilst simultaneously viewing voltage or current type signals in a power related environment.