Many markets have moved into a "buyer's market" and this type of offer is more common in a buyer's market. Seller's need buyer's now more than ever and are willing to accept a contingent sale offer more than in recent years past.
The seller will probably include a "release" clause from their side that outlines that if they get another offer before your home sells they will give you "x" period of time to release your contingency and move forward on the contract OR release them from the contract so that they can pursue the other buyer's offer.
These details vary state to state so check with your Realtor. If you have a seller willing to work with you, I don't see any reason to wait. Make sure your Realtor goes over the details of contingency.
You have some great advice so far. Another way to look at it is that if a seller is willing to accept an offer from you based on that contingency, then what do you have to lose? It your home doesn't sell, then you have no downside.
However, make sure that the contigency remains in force. The worst thing is to be a "have to" seller.
When it was the sellers market, the sellers will generally not accept offer contingent upon the sale of the buyers houses because there were multiple offers already, so sellers can pick and choose.
Now that the table has turned, the seller are happy to accept offers that are contingent upon the sale of the buyers home, especially if the house has been on the market for a while, or if the local market is very slow.
Although there are usually conditions attached - such as limits on how many days the sellers house will be off market, how soon the buyers house has to be on market for sale, how long before the buyers house has to be under contract, kick out clause where the seller can continue to accept offer and give buyer (you) a certain number of days to decide if you want to remove this specific condition, etc.
In addition, seller's agent will usually ask to come and look at your house, do a comp, to make sure there is a good chance that your house will sell before they accept your offer.
Sometimes, in a market, luxury home might sell faster than medium priced home or SFR sells faster than town home, or vice versa; so the seller might be willing to take a contingent offer.
There is a lot of variations to this. Make sure you ask your agent to explain the contract and consequences clearly to you so you are prepared for the situation - a bit more stressful, but for the right price, with the right strategy, it's worth it.