A digital scope is a must.
For starting out why is digital a must?
For starting from scratch, either analog or digital will be helpful. You simply MUST see what is going on. It may be cheaper to start out with a used analog than a new digital and, in fact, the analog may have far superior high frequency performance (like my $200 350 MHz Tek 485) but having used a DSO with 4 channels, single shot mode and decoding, I think I would rather leave the 485 behind if I could only keep one.
The advanced triggering, math and decoding are what make the DSO worth the cost. There are things you can do with a DSO that simply can't be done with an analog scope. The two questions are: Are those things important? Can you work around them? The probable answer to both is yes. There was a time before DSOs and, during one such interval of time, we landed on the Moon 6 times. So, sure, you can work around the shortcomings.
But why? Entry level DSOs are pretty cheap and they're fun to play with.
I'm coming around to the idea that buying a used scope is high risk. There have been a number of threads where the purchaser of an eBay special has been underwhelmed by what they actually got. I was lucky, my 485 has worked perfectly but my results are not indicative of the broader market. The DS1054Z is so inexpensive that it may not be worth taking the risk of buying a higher performance analog scope.
In the end, it's just a decision. There are lots of them...