The escrow period you speak of (the time it takes from the seller accepting your offer to purchase and your move in date) is usually negotiated between the buyer and the seller. I have seen them as short as two weeks and as long as three months or longer. A lot of the sellers decision to negotiate a shorter or longer escrow period depends on if they have a place they are anxious to move into or are, let's say, waiting for a new home to be built and maybe finished in 3 months time.
If everything is set for you, financing is pre-arranged and approved, I would ask for a shorter escrow period and that way, if they accept, you can get on with the move posthaste.
Congratulations to you, Slappy! Your first home! I'm really excited for you!