EMC/ Mains line filtering
The motor won't cause any harm when it's just running- spikes only happen when it is being switched. The power factor will be on the inductive side most likely. You might be able to get away with good design of your control board and an R-C snubber or a MOV across the relay contacts, but perhaps there is some regulatory requirement to do more in your jurisdiction.   

Electrically, the common mode choke you link to is rated for 12A DC, meaning it would be suitable for 12A RMS AC from a heating point of view. I don't see safety agency approvals on it though. The X and Y capacitors and the choke should be festooned with safety agency approval markings appropriate for that application (you must not use X capacitors or general-purpose capacitors for Y capacitors) and have file numbers available or it could be much more expensive to perform testing. 

One common method is to use a power entry filter, which would typically carry all the safety agency approvals and would be built into a metal casing. Two Y capacitors, one X capacitor and a common-mode choke. 



There are also line filters, which are similar electrically but without the IEC plug. 



Again, they have one X capacitor, two Y capacitors and a common-mode choke.