From a usefulness perspective I'd get a DSO long
before an LA.
What you use is a personal choice IMHO.
I've used DSOs (never owned one), both HP and Tektronix and never really liked them. I
use
an analogue 'scope only rarely in classic computer repair. But my (many) logic
analysers
are used almost all the time.
As I said, personal choice, what works for you is what you should use.
One thing though. No piece of test gear will do more than provide evidence of
what the circuit is doing. It will not tell you 'U38 is faulty' or whatever. You
still
need a good understanding of the circuit, how it should work and what you
should be seeing so you can tell if the 'scope or LA traces are right or wrong.
-tony