I agree with Dave (in video @6m45s) that the third most important (basic) parameter for DSOs is the memory depth, but as always there's a catch (or more). Don't just look at the memory depth specification!
Large memory depth makes it possible to sustain the effective sample rate at slow time base settings. Ideally, a 1GSa/s DSO with 1Mpts memory (per channel) would retain it's 1GSa/s from min time base setting to 100us/div, given 10 div screen width (10x 100us x 1GSa/s = 1 MSa) Thus reduced to 1MSa/s at 100 ms/div and so on.
However, this is not necessarily the case. It depends on the design of the scope, and it may begin to reduce the sample rate for instance at 10 us/div (#1). So, don't just look at the memory depth specification to decide which scope you should choose; be sure to test the scope and find out the break point yourself.
Also, note that a scope may not always use all it's available memory in real time mode! The specified memory depth may apply to single shot mode only (#2).
I use the term effective sample rate here, since the digitizer probably in most DSOs probably runs at full speed (as jahonen observed on the Agilent MSO6034A)
here. This is necessary for the glitch capture/trigger function.
I think that an "Effective sample rate" parameter could be an interesting figure in a scope specification. This parameter would reflect the sample rate used for displaying the data (typically Normal mode; not Average, etc, etc). That would also reveal weaknesses e.g. reduced (effective) sample rate in zoom mode. Or the other way round; to emphasize that the zoom mode utilizes the digitizer's max speed, as also shown by jahonen for the MSO6034A in the same post as above.
The importance of the memory depth I think must be based on the assumption that "everything else is equal", which often is not true. Large depth may not be compatible with high capture rate (#3), which also is a very important parameter.
#1: e.g. Agilent 1000-series (only 10kpts/ch but the principle applies). I had a look at it once and was truly disappointed...but then I didn't know it actually was a Rigol design
#2: e.g. Agilent 6000/7000-series. It uses only half memory in real time mode (at least with 8Meg option, I haven't checked the initial 2M standard depth)
#3: e.g.
Rigol 2072//C