How to decided which bridge rectifier to use?
Any (rated for the voltage and current expected) should work, but I suspect that high voltages may be developed from such a strong magnet in a large coil if shaken fast enough (perhaps hundreds of volts if dropped.) Of course, load will reduce this greatly. Test it using your proposed maximum shaking motion, and measure the voltage and current into a real rectifier / cap / load. May have to use an oscilloscope to see V/I accurately; a DMM will just show you averages, not peak values. 

Also note, the more load you place on the coil, the slower the magnet will want to move through it, which could hamper the shaking motion. You may find that 10,000 turns will produce a higher voltage and work better. Experiment with it. Once you know what's actually produced by the coil, then you can look at faster and/or lower-loss rectifiers to achieve a bit more efficiency. 

But say, if the coil is found to produce a peak value of 100v and the rectifier is only rated for 50v, then it may avalanche (conduct the wrong direction) and permanently fail. You want to get rectifiers that are rated for at least twice the expected peak voltage. So in this case, you'd want to get them rated for 200v minimum.