"standard" size for a double bass is 3/4. a size up from that would be 7/8, then 4/4. A size down from 3/4 would be 5/8, then 1/2, 1/4, etc. Generally (very generally), smaller basses are for smaller players (like young kids).
There really isn't an exact standard as to size, there are more general guidelines. One 3/4 bass might be a completely different size than another 3/4 bass, etc.
You want a 3/4 size bass. If you think otherwise, or have some special physical needs, your teacher will be able to help get an instrument that fits your needs. They'll also get you the techniques you need to not hurt yourself.
More links:
http://www.gollihurmusic.com/links.cfm