Each has it's unique properties.
Photo transistors are great for sensitivity, but everything else about them is bad. They're terribly slow, inconsistent during manufacture, and generally have poor linearity.
Photo diodes, especially the pin, are my favorite all around. They're fairly consistent, have a huge dynamic range, and if you're amplifier design is good, you can get great signal recovery. The trick is the amplifier. One amp is not good for all designs. Some amps give great bandwidth, but have poor noise characteristics. Some are of course the opposite. And then you have all the other considerations, like saturation and offset and such.
I can't tell you that much about avalanche diodes, because the only use I've ever had with them is for edge detection - and that design was prepackaged. I know that they're a triggered device, so don't expect to follow a linear signal with them. They also seem to be associated with high speed work, which is how I came across them.
Best luck,
Mike