So I have this receptacle and I have some 14/3. Do I need 14/2? Can I use 14/3?
Yes, 14awg is fine then if thats what fits your full load amps listed on your
name plate.
Double check to see if you need 240 with a neutral, in which case you will need 14/3 romex, black, red, white and a bare ground.
If no neutral needed then use 14/2, black, white bare ground.
14/3 allows you to run a neutral wire. Having that neutral would allow you to use one of the two out of phase 120V legs to have 120V feed to power anything that required 120V such as a fan. So you would have 240V and 120V feed coming from one 14/3 wire for example.