Instead of thinking about it as "selling a house" and "buying a house", you should be stating as your goal "getting from here to there".

A first time buyer who is currently renting, simply needs to coordinate their notice by the 10th of the month to insure a smooth transition. 

But those who currently own and are moving to a new house, require a completely different strategy.  Before you go out to look at homes to buy, you should get your home completely ready to sell.  Using the same real estate professional to sell your home and to buy your new home, particularly if you are staying in the same area, is a great advantage.  Have the agent come to your house before you go out looking for homes to purchase.  Complete everything on the agent's checklist needed to insure a fast sale at a high price.  Then go out and look at homes. 

If there are several for sale that you like a lot, then list your home in the mls before you make an offer.  Since you have already prepared it for market, that should take about an hour.  You should not have to go into temporary housing by selling first unless you have a particularly difficult property to sell. If you are not getting good activity and feedback, be quick to make changes needed and as recommended by your real estate professional. 

Weekly evaluations are in order after the first 10 days on market.  You should be able to sell your home and buy your new dream home in short order, if you have a good agent and remain open to their suggestions regarding the property you are selling.