in this economy and the current auto industry, i'd try to sell it private party and pay off your loan first. if you trade it in and get less and have the balance rolled into your new car financing, you'll always be behind and have negative equity in your car.
i'd do all your car research, find the car you want, then put your car on the market, so when you do sell you know exactly what you want and can do a quick turn around.
leasing only works if you drive 12-15K miles a year, your used to getting a new car every 2.5-3 years, and if you are willing to always have a car payment.
personally, when ever we get a car, we always finance it over 60 mos (to get the lowest monthly payment) but do extra payment and pay it off in about 3 years (make sure your loan doesn't have an early payoff fee). this way if one month we have house repair or something big come up we have the option to just pay the actual monthly payment. but normally try to do extra payments each month, or if we have a bonus check come in or something, we do the regular payment every month and then throw the bonus check as a big lump sum to it.
we keep the car for 6 years, and have a payment for 3 years. once the carpayment is done, the other person gets a new car. so we always have 1 carpayment and it alternates every 3 years for who gets the new car.
and we ony have 1 car payment. does that make sense?