I recently got married and applying for my H4. We would like to know if I can choose the first available appointment (while he applies for his H1B extension as the visa expires on September 30,2016)? In the DS160 form I have mentioned my stay dates as per his current visa duration. So if he applies for extension during the visa wait time, would this effect the processing of my VISA?
You can apply for H-4 visa using his current petition. Your visa (if approved) will be approved for the same duration as current petition.
If you enter US using his current petition, then you would receive I-94 based on current petition and it would expire in next 3 months. So H-4 extension would have to be soon applied.
If you enter US using his extended petition (and visa stamp based on old petition), then you would receive I-94 based on new petition and no H-4 extension needs to be applied.