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Personally, I think emotions would be more intuitive/easier to choose from than numbers. However, the number of emotions to choose from would have to be low (I'd say 4 or 5). I can see why you'd want to use numbers for analysis, but you can assign a value to each emotion as well.

A list/grid of emoticons would be fine for displaying the options. Nike+ does something similar to this when it gives you the option to say how you felt during a workout.

"What do you think would be the best way to display the emotions?"

Why don't you just list them in a dropdown? I usually dont understand emoticons unless they have description etc. But thats just me :)

Take a look at alpha.emot.io by @nickwsmith

Nick has done a lot of research on this field and with early cstomers. If you don't know him already shoot me an email and I'll do an e-intro