Hi. Maybe post a link to, or an image/schematic of, the motor circuit you wish to use, it's hard to give a precise answer otherwise perhaps as there are so many variations.
These are just very basic rules of thumb: If the motor is 12V, then any transistor rated - at the very least and not recommendable - over 12V constant operation, but it'll maybe get hot quickly and so in my little opinion rated at least 2 -3 times the motor voltage and that can handle at least an equal amount of current as the motor needs when running. Transistor datasheets should show the constant current possible and (let's call it) peak momentary current - bear in mind motors draw a lot of current at start-up, and I guess the diode is for back emf.
The diode is also hard to answer without knowing the motor specs other than arduino signal (I also guess that is 3.3V max.) + 12V, but maybe something as simple as the 1N4007 rectifier diode would be ample, so long as you have no need for high speed switching. I know the 1N4148 high speed switching diode can come in a 400mA version, but I'd derate that to half, i.e. 200mA max. I like derating, amongst other things the components last longer.
I'm not a good designer to follow as I'm a hobby learner, and everyone has their own "do it this way" manner of making circuits work, but to derate I'm sometimes happier to use 60V, 4A constant current BJTs for 200mA loads than a supposed 800mA transistor..., that way you avoid the need for a heat-sink, and as I said, the component should last a lot longer.
If the motor is low current (50mA), you can save yourself work and use a half h-bridge IC, the L293D is one I know, and other people will know far more powerful ones - those drivers/ICs appear in threads here as IRxxxx (e.g. IR1550 - don't know if that specific number exists, but that's the format) a lot of the time. These devices can be harder to get working right, whereas a single transistor + díode for a uni-directional motor is quick and simple to get working.
You could use a MOSFET, and skip the protection diode, e.g. ZVN4206, it can be used to interface between driver circuits and motors.
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Sorry, but re-reading your post, something is not very clear: Just noticed, "mains powered motor"? Is the motor AC or DC? - if AC then you may need a relay - either mechanical or solid state. Where does the 12V come from - is it the mains supply? If so then you would need an appropriate transformer to reduce the 220V to 12VAC, or if it is DC, which I'm assuming, then any AC-DC wall adapter is the simplest option...