Once your employer applies H-1b on April, you will be eligible to work from October 1, 2008 (provided it gets approved). Till that date you have to be in the U.S. on a valid status.
On the other hand a Green Card process for a specific employment based category can be started by your employer at anytime. The first process is PERM Labor Certification, followed by I-140 (immigrant petition) and I-485 (adjustment of status). The last one can be filed only if your priority date (date on which the labor certification is filed) is current. Once all of above petitions gets approved, you obtain the green card.
Case processing time varies widely based on case complexity and background check. Being from India calls for longer wait times owing to the increased number of applications. At this point it is difficult to predict the wait time as applicants with priority date as early as 2002 (or even earlier) are still waiting.