Neither of the possibilities you mention capture what I hear when a French speaker says j'ai. In fact, the audio links in the lesson don't at all sound like the i- "ice" to me. If I were to come up with an English analog, I would say it is like the e- in "enemy", maybe drawn out a bit to lengthen the sound.

Whatever you choose, the sound in the audio is a pretty darn good rendition of what it really ought to sound like. Best to take this as a template.