H1B grace period questions

My company did layoffs two weeks back and I was affected by the layoffs. I got one month of notice period (they will run my payroll for a month). I have a few questions on the H1B grace period I read online from the USCIS website, the grace period is 60 days. I’m afraid I won’t have any offers in the next few weeks, I might get into a grace period. Getting a job during the grace period will have any implications on Green card processing in future? I have GC priority data in 2013 June.

I might have an offer in 3-4 weeks from now and the H1B transfer process another 2-3 weeks, total it might take 6-7 weeks.

Will my grace period end on the day my company fills for H1B or the day I get the salary ?

Any suggestions will be appreciated.

thanks in advance

Your grace period starts after your last paycheck date. Your GC process is not impacted and has nothing to do with your H1B job as the GC job is a future job offer.