There's a slightly higher risk of mammary cancer over her lifetime if you wait til the second cycle. Most vets recommend spaying at 6 months, just before the first heat. There are several reasons for this -- the key ones being that many owners find it difficult to manage a dog in heat and totally isolate her for 4 weeks inside with no contact with other dogs, no walks. As Bruce has pointed out several times, it is always a risk to take any female in heat outside. I do know of cases of people with a female in heat being assaulted by very large loose male dogs who are desperate to get to the female. There's also the issue of the dog dripping blood in the house. And there's always a risk of pyometra following any heat cycle.
On the flip side, some feel that it is better to wait til she is about a year old -- eg between 1st and 2nd heats -- as by then she will have completely stopped growing. This is of course an option for a careful owner willing to manage their dog in total confinement for the month of heat. There's some evidence an earlier neuter or spay may cause the dog to grow fractionally larger --a half inch or inch taller perhaps.
Having read a lot of the pro and con material, the minor cons of spaying (or neutering males) regardless of age are easily balanced by the cons of leaving dogs intact, and for me remain strongly outweighed by the fact that I know from experience how easily accidents and unwanted pregnancies happen, I know how inclined most people are to find a heat to be a lot more difficult than they imagine to manage safely, and I feel that far more injuries and deaths (including euthanised unwanted puppies) are caused by unneutered male and female dogs escaping from homes, wandering, getting into fights. I know of regular occurences of female strays in heat, often very small dogs, arriving at the pound covered in lacerations and in severe distress from being pursued and assaulted by gangs of loose males who could scent her from a mile off. As Bruce has noted, a female can try just as desperately to get out to go find males as the males will try to get into back gardens or houses -- including leaping high walls. And all this is made more complicated by the fact that many owners do not recognise their female has gone into heat until the unwanted happens. I have even had vets fail to recognise a dog is in heat because sometimes the signs are very subtle, especially first heats.
Whether to wait til after the first heat really comes down to how cautious and responsible the owner feels they can realistically be. Many owners do not find they can manage that long confinement for their dog but others are happy to tolerate the inconvenience. Personally, I would never home a female rescue on the basis that the new owners manage her through a heat because I know how difficult this is, having had several females come into rescue during a heat. I always spay.