Two different instruments. For voltage measurements, a DMM has a lot better accuracy than a scope.
Ummmmm. Yes, it's probably why they have different names too.
But... A oscilloscope IS, by definition, a voltmeter with an axis for time added; plain and simple.
Accuracy, I think it would depend on your equipments original specifications and current condition, no?
My point being,
if on a limited budget spend it on your signal generator and your scope,
a better DMM can come later, and is also highly useful. You can do most everything with a scope and more - just with a scope only, you may have to do some math (to get resistance, inductance, capacitance, transformer hysteresis values etc.). This was in reference to a choice of DMM instead of a scope -
and budget related. Not looking for an argument, only clarifying for newer members that may not understand. That old book I suggested tells you how to get all of this out of your scope and more.
Also, correct me if I am wrong, if measuring AC with a DMM... Say you are matching output on a stereo pair using a nice clean 1K signal from the decent signal generator suggested. If your unit under tests power supply is leaking AC or ummm wifi etc., is getting mixed into you amplifier and likely amplified, the AC you are measuring is often cumulative in a DMM's RMS measurement, there could also be DC offset present. With a scope, you can SEE the unwanted AC on your 1K signal. You can then zoom in and figure out where the frequency is and track down the source quickly. With a DMM only - this could be VERY tedious, if not damn near impossible - and by impossible I mean NOT WORTH THE TIME.
And FWIW - we keep our computers and converters OUT of our test equipment signal chain - we encountered too many issues in our formative years trying that. YMMV.