I’m not an expert by any means, but I’ll throw this out there.
Fast Blur. As the name implies it render fast, however it’s not as accurate as the other blurs.
Box Blur. Renders take a bit longer than fast blur, but it’s more accurate than fast blur.
Gaussian. The most accurate of the three. Longest render time of the three.
Compound blurs and Lens blurs require an additional layer (map) that’s drives the blur. These blurs are more complicated to use, but can produce some interesting results.
That’s way over simplified, but it can help out when deciding which blur to use. Fast blur works fine in many instances.