Short hair can mean anything from a close crop to a bob brushing the jaw, so it helps to decide what you want to expose, keep or simplify before choosing a name for the cut.
How short do you want to go?
A pixie keeps the overall silhouette compact. A bob leaves more perimeter length. Shags and bixies sit in between, depending on how much movement and length you keep around the crown, ears and nape.
Think beyond the first week
Short cuts can be fast to style, but some need more frequent trims because small amounts of growth noticeably change the silhouette. Ask how the cut should look as it grows and whether it can transition gracefully into a longer shape.
If you want texture
Start with shaggy pixies or messy short choppy hairstyles. Both can look relaxed, but the cutting plan still needs to respect density, natural movement and the amount of styling you want to do.