There are several advantages to having a dog via a reputable rescue. Especially if you have DC, rescues will take the time to assess a dog's behaviour in a family home, usually via an experienced foster carer. They can also give you a more detailed, honest assessment of their behaviour, and will usually have access to free behavioural advice, training support etc if there are issues.
If for any reason the rehoming breaks down, rescues will ALWAYS provide a safe place for the dog to go, even if it's many years later. As an example, we fostered a dog back in 2008, who then went to a very loving, secure home. However, several years later, the owner had major and very serious health problems, requiring a lengthy hospital stay. The dog and it's housemate came to us for foster care while owner was in hospital - an enormous relief for the owner who knew they were safe, together and cared for. Sadly, the owner's health continued to be very poor, and they made the decision to surrender the dogs permanently. The dogs stayed with us as long term fosters, with full rescue back up. One passed away late last year, but the other one is still with us. The original owner still has regular updates and news and is delighted that their dogs have managed to live their lives in a place of safety, well cared for until the end of their days.
I also know of rescues who can offer services like emergency short term foster care when owners are having major problems as well as other useful services like access to secure off lead areas, and contact with other owners for things like dog sitting arrangements.
Taking on a dog from the ads is a real gamble - I would consider it only if I was an experienced owner with no DC, who was willing to cope with and work with difficult behaviours. Adopting via a rescue is much easier, more straightforward and gives the longer term support I discussed.