I think you are putting the cart before the horse. You will be in a much better position to buy a home if you first have your own on the market, and ideally you should have a contract on it before you make an offer on another home.
In the situation you described, you are getting yourself into a bidding war, and it is one that you really can't win. Even if you get your offer accepted, which is a real longshot if you make the offer with a contingency, you still have to sell your home before you can buy the new one. Only now, you'll be selling your home under pressure.
If you're serious about moving, put your home on the market now. You can go ahead and start looking at homes with your Realtor in the meantime, but wait until you have a contract until you actually make an offer on a home.
I've seen too many people do it the other way, and it goes a whole lot smoother when you sell first and then buy.
Good luck, and if you have any questions, you can email me at: Bob@SellitWithBob.com