Regarding H1 visa for postdoc

[navinprakash]

Hi,
I have been offered a postdoc position in one of the universities in US (computer science department).
They are sponsoring H1 visa. I have never been to the US before.
They are yet to start processing the visa as I got the offer letter only yesterday.
How many weeks/months will it generally take to get the visa?
I want to join the lab by January 1st week. Will it be possible?
Should I ask them to give me J1 visa instead - will it be faster?

[inadmissible]

With premium processing, H-1B is no slower than J-1, without the attendant disadvantage of the J-visa Home Residency Requirement