Remember! Moving day will come sooner than you think, so get planning now.
It may or may not be practical to move in on the closing date. You may not get the keys to your new home until late in the day. So you may want to try and schedule the actual move for a day or so after closing. If you intend to move at the end of the month, contact a moving company or truck rental company now before they're all booked. If you can move mid-week or mid-month, a moving company might cut you a deal. Go with a reputable moving company. Go with an established, insured mover, so your items are protected.
Pack it yourself, and pack early. Nobody will take the same care you will. Start early and spread it out over many days. Label all your boxes by room so the movers know where to put them, and label anything that's fragile.
Do you really need to take that with you? A new home is a new lease on life, and a chance to liberate yourself from stuff you simply don't need. If you haven't used it or worn it in the last year, you probably don't need it. Have a garage sale, or give it to charity.
Once you move in slow down! Take time to get a feel for your new home, and more importantly, your new budget. Take a deep breathe and enjoy what you have, your new home.