The following items are something I consider important after you received your green card.
1. If you still work for the same company and the prevailing wage is larger than your current wage, try to match the prevailing wage in your payroll for the first 6 months after you reveive the green card. Note: small difference is fine, over $10,000 difference is not.
2. Stay in the same company for at least 6 months after you received the green card and you can take off after 6 months. This is the way to save you any possible trouble when you apply for citizenship in 5 years.
3. Give your green card copy to HR for your employment profile update.
4. Read the rest in Pijiang's blog or the letter in the green card mail.
P.S. to fulfill #1 & #2 will save you any possible trouble when you apply for U.S. citizenship in 5 years. We never knows what will happen, but we do know sometimes, shit happens.