My fiancé lives in Jamaica and is a b1 visa holder.I need to know if it would expedite matters to marry him in Jamaica then file the appropriate paper work or could we get married here and he returns to Jamaican while the paperwork is ongoing
Also I am only a permanent green card holder who will be eligible to file for citizenship in December,would it be better to get married prior to obtaining my citizenship or after

Much faster to wait for you to be naturalized and then file.

After I obtain my citizenship and file for my now husband is there a procedure that will allow him to stay in the U.S with me while his papers are being processes since he is a current b1 b2 visa holder and does it make a difference in processing time if we get married in U.S or jamaica since he has a b1 b2 visa?

If you are a USC and you are married and he is in the US, then you can file the relative petition and he can file the AOS concurrently. Please note that this does not give him lawful presence beyond the date on the I-94.

The timeline is much faster here in the US as you can file it concurrently. If you marry in Jamaica, then you will need to file the I-130 first, then for a K-3, he then must apply for the K-3 visa to enter the US and then file the AOS.