Bridge, or full wave rectifier?

A bridge rectifier is a better option at this ampearage. U need to have a good filter circuit as there is every chance of the DC motor being subjected to fulctuations with the ripples.

I suggest a LC filter or a pi filter as good option.

These will give you a good DC voltage. A single capcacitive filter will be of first order and the ripples may not be smothened properly. A filter of second or more order will be good.

A full wave rectifier will likely do the trick for a motor. Bridge rectifiers are usually called for when you are working with more sensitive electronic equipment that needs less ripple in the line voltage. Unless the motor is some type of stepper motor, a full wave rectifier should do.

Bridge and full wave rectifier do the same thing. Depends whether you have secondary of your transformer with the middle point (in which case use full wave rectifier with two diodes) or if you don't have middle point use bridge. In both cases you need capacitor. You wouldn't harm the DC motor by a bit ripple on your DC voltage (if you don't have large enough capacitor).

The pulsed DC coming out of the rectifier would generate heat in the motor and wear it excessively. A capacitor will buffer the fluctuations, and result in smoother and more reliable operation.

It will depend on the transformer's output firstly

For full wave, hope you have the mid point in the secondary winding

Bridge can be used in either case, but full wave requires three secondary leads

I suggest a bridge because theoretically, efficiency is higher

I assume that you have taken care of filter etc.

So you propose a rectifier with only D1 and D2 ? You try to short D3 and D4. Please draw your "genius" circuit. The negative DC wire would connect to both AC wires directly and therefore short the AC supply. In the same way as D1 and D3 are ON at the positive half-wave of the AC input, so are D2 and D3 on for the negative half-wave of the AC input. In the same way as D1 and D4 are feeding alternately the positive DC output, so are D2 and D3 feeding alternately the negative DC output. If you don't see this, then try to draw more of your simplified circuits and use color pencils to visualize the current. Suggestion: Red for positive, blue for negative (and black for your short circuit).

To be practical, go for the full bridge. It is found today as an encapsulated part, any specs you need, and about cheap as dirt.