Another vote for frozen fruit over ice. If your berries aren't freezer burnt (burned?) they shouldn't make your smoothie taste weird.
And fresh isn't necessarily better when it comes to fruits/veggies. The difference being that frozen produce is frozen shortly after being picked, which can help retain nutrients that would otherwise be lost over time in fresh veggies during transport, etc. Of course with frozen you are sacrificing texture, etc but that's not really an issue with smoothies.
One of my favorite smoothies is simple: one banana, about 6 good-sized frozen strawberries, 1/3 coconut milk, topped up with almond milk.