Receiving any offer, especially your first offer, is exciting news! Call your seller and let them know right away. Depending on if your seller has recently done a transaction, they may want to meet in person to go over the offer and for you to present it. Print out a complete copy and have a meeting.
First thing to look for is if the offer is complete. Does it have proof of funds, if financed, a preapproval letter, and if a lease the credit report. It is a good idea to call the lender who preapproved the buyer to ask them some qualifying questions. Is the bank one that you recognize? Have these buyers written any other offers- were they accepted? If so did they cancel? These are great questions to ask the buyers agent. You are entitled to ask them to tell you about their buyers.
When reviewing the purchase agreement, the first page has all the important information. The Purchase Price, Financing terms, close of escrow. Make sure that there are no hidden terms that will affect the net of the seller, such as excessive home warranty plans, buyer request for seller to pay closing costs, strange contigencies such as contigent on sale of other property (this can be doable if the property is already in escrow). If the offer is solid, then it is a good grounding point to start from there. If the offer is strong the seller may accepted it. Or they may decide to write a counter offer. A counter offer voids the first offer so be careful- if you sign you have acceptance, if you counter the buyer then must sign to have acceptance.
double check the expiration date to make sure that it is the standard 3 days.