Younger players generally start on alto or tenor, sometimes bari, but not usually. I highly advise against a beginner starting on soprano (child or adult) as the embouchre is much tougher and harder to control. You can't objectively say that alto or tenor are better for jazz, but I think that tenor is the way to go if someone is set on learning jazz, specifically.

I've got two affordable tenors for sale in the free trading section if you're interested.

I would suggest Tenor, and along with it Lessons. I would also suggest you start learning basics like you where going to play classical first. I diddn't start playing Jazz untill my third year. And I've got to say that I wouldn't be hlaf as good at jazz if I diddn't start out playing mozart, and betoven, and tchecovsky (I know I diddn't spell their names right, but I'm a musician not a writer) you need a classical backround before you can start on the fun stuff. Start with your major scales, then minor scales, then blues scales. And practice arpeggios. Scales and arpeggio's are the basis of any jazz solo. And even though It's tough and sometimes boaring. Don't just give it up. It really is worth the practice when you start playing well.