Best way from L1B to Green card with new employeer

[pbolliger]

I currently have a L1B Visa and have a job offer from another US company. How long does it take to change to H1B visa and what are the dates we need to look for ? I have read that April is key, but even if approved I can't work for the new employer until Oct ?
Can I also apply directly for a EB2 instead ?

Thank you for advice given