Need advice before moving to tokyo

Moving to Tokyo to work for Japanese company for 1-2 years. Should I rely on shakai hoken from employer for medical insurance or take international medical insurance instead? What is the reasonable rental allowance to ask? Location is in Saitama, am I better off to rent in Saitama to reduce travel time to work or enjoy Tokyo quiet suburbs, but travel longer?

Personally I'd prefer to live in Tokyo. Apart from being more fun, you'll avoid the commuting where chances are you'll need to stand all the way.