The sunnah is to shave the head as the Prophet has made Duaa three times for those who shave their heads that Allah would have mercy on them.
It is permissible to cut the hair short by clipping it from all sides. No specific length is prescribed.

If i go for hajj and get my hair shortened instead of fully shaved, are there any restrictions, such as the hair has to be one inch thick? This is what i hear from some hanafis.