I think Shrikes are a great alpine ice tool for the beginner. They aren't great, but the price is right. I'd get a straight hammer and a bent shaft adze. The hammer is useful for placing pickets and pitons. The adze for chopping belay platforms and clearing surface crud when placing screws.
Then, if you want to graduate to frozen waterfalls, you can pick up a curved shaft tool, like the Viper or Rage, to use with the bent shaft Shrike and you are ready to start. If you find you really dig waterfalls, you can buy a fourth tool with curved shaft. Now you have an alpine set and a frozen waterfall set.