A logic analyzer is a great tool, particularly if it accepts a 'state clock' instead of a random clock generated internally. But...
The scope will probably get 10x the amount of use of the logic analyzer even if the project is purely digital. As stated above, if you want to see how things really work, you need a scope. Can you work around it? Sure! But you're missing out on another form of learning - seeing.
Even the simple experiments like the charging of a capacitor are left as hand waving because there is no visible action. Yes, you might slow things down and watch it with a V-O-M (or, for an ugly solution, a DMM) but it's not the same. Just take a resistor in series with a capacitor and hit it with a square wave (eg from an Arduino) and watch the rise and fall curve on a scope. Input to resistor, one side of capacitor to ground. Probe the junction of the resistor and capacitor relative to ground.
Now, here's something fun: You formed an integrator in the experiment above, turn it around and create a differentiator. Run the signal into the capacitor in series with a resistor to ground and hit it with a square wave. Again, look at the junction of the resistor and capacitor relative to ground. You will see a positive going pulse at the leading edge of the square wave and a negative going pulse at the falling edge.
Even the most elementary circuits are a lot more fun with a signal source (even an Arduino) and a scope.
That new Siglent SDS 1000X-E 200 MHz 2 Channel scope is looking very attractive at $379. That kind of scope will cover electronics for a very long time. It has the bandwidth advantage over the other favorite, the Rigol DS1054Z. It doesn't have as many channels as the Rigol so there is a tradeoff between bandwidth and channels versus equivalent $.
I don't see where you can go very far in electronics without a scope. Maybe not day one, but soon...