If you're living in a market where some houses are going for $150K over asking, then you MUST buy before you sell. In a seller's market, you will get multiple offers on your current house when you decide to sell, it will sell for (well) over asking, and you can dictate possession dates. You do not need to worry about selling your own home, if you have a competent realtor.
But buying a home is an entirely different story. You may struggle to find something affordable, and there may be multiple buyers each time you decide to make an offer. You may go through this cycle several times over many months before your offer is accepted. You should do this while living in your own home, with the comfort of knowing that you can sell your own home easily at any time, instead of the stress of an imminent closing date on your own home. Or worse, move into rented space or Malvolio's mom's house for months or a year while the market increases by 15% and the houses in your old area are now selling for $100K more than you sold for. Ouch, now you really can't afford to buy what you want, and you may end up buying something equivalent to what you used to own, for more, plus legal, realtor, and land transfer costs.
If the closing dates don't align, then bridge. This will only end up costing a few hundred dollars, less than $1K including legal fees (the lawyer will also charge to handle this). But by buying before you sell, you'll easily make up that difference.
This advice only applies to hot property markets. I'm not a realtor, just a guy living in the GTA who went through this process last year. Lost out on three offers over 10 months, then bought for asking price on fourth offer (very fortunate), then sold for $90K over asking, then bridged for 2 months. My realtor is awesome and made the process as stress free as it can be.
Get a good realtor, start house hunting while preparing your own house for sale, and enjoy the process. Also you should negotiate with your realtor, they may be willing to reduce their commission on your sale if they are also representing you on the purchase.
P.S. Do not make a contingent offer, and do not accept one. Get your financing in place before you make an offer, and if you are concerned about inspection, you can also do that before the offer, if you act quickly. The inspection will cost ~$500, but it will increase the value of your offer by much more than that since you will be going in without conditions. I spent ~$1,000 on two property inspections on homes I lost out on, and I don't regret it. That is the cost of doing business. The other offers on the home I eventually bought were for significantly more than my offer, but they had conditions. I saved at least $40K by being condition free, and I only spent $1,500 on three property inspections. And, some people will just drop out of the multiple offer scenario when they learn that one of the buyers has done an inspection.