The main diode specs you care about are current rating and peak inverse voltage. To get 300VDC, you need around 220VAC input. That is about 300V (peak) and 600V (peak to peak). 300V diodes will not be safe to use. I recommend 400V diodes.
The diode (and AC transformer current) is always higher than the DC current which you say is 3A. I think the diodes need to be rated for at least 5A, higher is better. They will also need to be mounted to a very good heatsink. I am not sure why you need a 40A bridge? That would be huge.