What to do?  Should I sell and no where to go or should I buy and then not be able to pay for it because I can't sell my home?  You worry too much.  This can be handled quite simply.   

Of course you should not end up owning two homes.  The cost is impossible for most people. So lets look at both options.  

Buy First and Then Sell -   This approach usually applies if you have a very specific type of home or location in mind. If you are willing to take what is on the market then this is not the option for you. If you decide to buy another home and then sell your present home, you will make your offer "subject to the sale" of your present home. This will give you the confidence of knowing that you have another home to move to when yours is sold. This factor is obviously the primary benefit.

You feel comfortable, but the purchaser of your home may not.  The vendor will be putting and this puts them on hold while you find your new home.  What are they to do?  Well, they will insert an "escape clause" which allows them to accept other offers while you try to sell your home.  If another offer comes in you may either remove your condition of sale to firm up your offer or you can just walk away and lose the house.  

For the vendor this situation is less than desirable, because it makes the vendor's property a little less attractive to other buyers who will not be that interested in putting in an offer that may be of no effect.

Either way, there is stress on both parties and that is never helpful in negotiations.

Sell First and Then Buy -   The big disadvantage here is that you have little idea of where you are going to live after the property is sold.  Having no place to go - to be homeless - is not much of an option. 

However, selling first gives you a clean shot in negotiations for your next home.  You have the money and are ready to go.  Vendors like that, .... a lot.  If you are concerned about finding the right home you may insert a clause which gives you time to find a new home.  This puts some pressure on the purchaser, but if you need the clause, don't be afraid to ask for it.

Third Option - It may be possible to own two homes at the same time if you are able to get bridge financing using the equity of your first home as a down payment on the second home.  Discuss this with your lender when you go to be pre-qualified for a mortgage.  If you are not in need of a mortgage, you are nearly assured of getting bridge financing.