The rule of thumb for low carbon steel is 1 x thickness is the minimum bend radius. There are special cases though. Reducing the carbon to .05-.10 improves the bendability and bending across the grain will allow smaller bend radius. These assumptions are for air bending where the die opening width is 8 times the material thickness. If the die opening is greater than 8T than the radius on the part will not match the punch and will not be a smooth radius.
In practice unless you are willing to spend additional money for non-standard bending tooling you will be bending 14ga with a 1/16" radius punch and utilize a 5/8" vee die. You could probably use a 1/32" radius punch however the part will come out with a distorted (non-radius) bend and the punch will have excessive wear.