Logic analyser or oscilloscope?
Once you've got a bomb-proof digital system going, then a logic analyser is great if you want to see complex signals across wide busses, or time, or codes.
Until you've got said bomb-proof system going, an oscilloscope is essential for figuring out why your so-called digital system is behaving in an analogue way with ground bounce, logic overshoots, slow edges causing multiple clocks through oscillation.
A two, or preferably four channel scope can handle enough signals for de-fleaing I2C, serial and SPI communications. Even with wide busses, a clock, a strobe and a couple of MSBs are enough to sort out what's going on.
If you only have bench space or resources for one instrument, get a scope.