H1B - I-120 Case Approved, Passport Expired by Dec 2016

Hi,

My company had applied for H1B petition this year (2015-16), my petition got picked on lottery and recently I have received email from USCIS saying that my Form I-120 has been approved. By this I hope I am eligible to work in US from October 1st 2015 onwards legally. So considering my passport is valid for more than 1 year from the date of entry into United States, is it possible to apply for new passport in US or I should apply for renewal before I start my travel to US.

Similar condition for my spouse too. My wife passport expires by Oct 2017. But on the current passport, there is no spouse name added. Will it create any issue while applying for H4 or on her stamping.