Allow me to illustrate why I feel an analogue scope is still very much worthy of serious consideration compared to an entry level DSO.
When my own scope first came out, the idea of an 'analogue-like' graded intensity display on a digital scope was still new - not to mention expensive - so it has a button on the front panel which allows it to be switched on and off. Tektronix call it "digital phosphor" mode.
With it off, it behaves much the same as many modern budget scopes; it takes one sample per pixel and displays it. With it on, however, it samples at a much faster rate and displays a trace whose intensity at any given point is related to how often the signal being observed is actually at that level. The trace is much more like what a true analogue scope would display.
Here's a capture from a circuit which I currently have set up on my bench, with DPO mode turned off - ie. the sort of trace than an entry level DSO would show:
...and for comparison, here's the same three signals re-captured with DPO mode turned on:
For the two simple digital signals there's clearly not much to choose between the two, but for the analogue signal on ch 2 there's a world of difference. With the analogue-like DPO mode turned on, you can see the regular short duration spikes that the scope simply misses without it because they're not as wide as a full pixel with this time base.
What you also don't see is the difference between how stable the two traces are. With DPO mode on, the trace is rock solid, and virtually identical on every sweep - but without it, the short spikes in praticular come and go with each sweep, dancing up and down depending on whether the scope happens to be sampling at the instant they're there or not.
In 'simple' digital mode, the trace just doesn't really represent what the analogue signal is doing, and that's why I'd rather have a good used analogue scope than an entry level new DSO.