Although this question is from 2010, it is an important question when trying to juggle both selling and buying at the same time.
Since your current home is paid off, you can stay put and search for a new home. Rent this home and then use the proceeds to contribute toward your new larger home. Or if you need the money from this house as a down payment for you new purchase...price it correctly, make sure it shows well and get it on the market for sale.
Remember....if you have to sell to buy, most sellers are not going to wait for your home to be "in contract" to strike a deal with you. So be proactive...get your home on the market and sold. You will be in a much better position to purchase the much larger home you desire.