When should a blender be used instead of a food processor or instead of a juicer? I'm planning on investing in one of them. I would use if for making smoothies and beverages. I've got a Magic Bullet which I put frozen berries in, but find the consistency is too thick to drink.
The three types of appliances you have listed have different primary uses, and best purposes, although they have some overlap in their capabilities.
Blenders. Good at, well, blending: making smoothies, pureeing soup, grinding nuts to butter, and at the high end, making frozen ice drinks.
By far the best device for this purpose, but not very versatile.
Immersion Blender also known as a stick blender. You didn't ask, but this device is very good at most basic blending tasks, although far less powerful than a full sized blender, especially the top of the line ones. They are very effective at pureeing soup in the pot, or doing a quick puree on a tomato sauce, for example. They are also good for small quantities of smoothies (at least the kinds without ice) where you can blend them directly the glass.
Convenient and often less hassle than a blender for small blending tasks, although not as powerful overall.
Juicers Good for extracting juice. The main difference from a blender, which simply purees everything, is that juicers attempt to separate the solids from the juice.
I have never heard of a juicer that operates on frozen produce.
I won't comment on specific types of juicers as I am not expert in that area, and that really should be a question of its own.
Food processors Very versatile, depending on the blade or disk. Can do almost everything a blender can do except frozen drinks, although perhaps not quite as well. Can also slice (much like you would on a mandoline), shred, and chop. Also useful in some bread and pastry making for working the dough.
Note that if your frozen berry puree is too thick for your liking, a different appliance is unlikely to change that. Instead, you will want to either add some other liquids (like water or apple juice or yogurt) or let the berries thaw a bit.
You will have to decide which appliance will best suit your needs. Based on your comments on what you will use it for, a blender might be your preference, although you might prefer the convenience of an immersion blender if you are not blending frozen drinks.