What height to set baseboards before carpet is installed?
3/8-5/8" but most 1/2"

Reasoning:


you have padding and carpet.  With a plush carpet and pad you might be at almost an inch or even over.  
you don't want the tuck to be so tight that it looks like the carpet is being smashed under the baseboards.  The carpet should look like it is just flowing under.
Note that most floors aren't exactly flat.  So make sure you are measuring this gap every few feet so that it doesn't become too big or little.  
We actually have little wood blocks that we use when setting the baseboards to keep consistency.  We knock these out after a room has been nailed.
Completely ridiculous to put baseboards in after carpet.  If I am doing a complete gut I want the baseboards in, nailed, spackled, and repainted where needed.  I don't want paint on new carpet or guys walking around on carpet.  We carpet just a day or two before open house.