There were survivors in the few first cycles maybe. Or so I'd assume. I don't remember exactly but it is said or heavily implied that the Reapers built both the Citadel and the Mass relays. They learned from their mistakes and even though they are machines with nothing but time on their hands they made sure every single species who made it to some kind of space era would evolve the way they wanted and would end up being easily harvested (or at least things would be made easier). We do have an example in the form of Leviathans of a species capable to survive not just one but many cycles (creators or not things are the same for them and every single other species, they are harvested).
If you think about the Reapers objectives, I doubt they would make planets inhabitable maybe a couple per cycle when the ennemy is kinda "too tough" (I think I read about it being done during the Protheans extinction but I'm not certain) but those planets would have time to get back to a state where they will be able to support life. So they'd poison the water or whatever but I doubt they'd go all Death Star on the planets.
Plus the number of surviving members required for a species to be able to live on is wildly different from one species to another. Take the asaris, you'd just need one single asari to survive for the species to survive. On the other hand humans would need several thousands souls (it's a guess) to be able to maintain an healthy population with a diverse pool of genes. Plus, when you say that the survivors and their children would have a headstart in developping themselves I'm not so sure. Here you have two situations either a groupe of random humans (let's take them) survived on some remote colony world. They will be able to tell their children about some things, what they witnessed and so on but will they be able to build a spaceship ? Or some kind of computer. Sure they'd probably have some remnant of technology but picture this tomorrow the world as we know it ends, everyone who knows how to do specific things like computer composents (or planes) died. We don't have access to internet anymore and nothing more than you little town library... We might be able to make some electricity (thanks science classes) but rebuild the internet ou computer might take a couple generations probably more. And I'm not talking about very scientific things.
Or you have something akin to what the protheans did. Selected people, representatives, the best in their domains are selected to become the weapon that will end the cycle once and for all. You might get back some level of technology faster but I'm not sure things would follow. Especially if we take our world for example. I mean... How many top scientist would be able to pass on their "superior knowledge"... And I'm pretty certain education would not be a top priority in the profile of people selected to rebuild humanity. Though, this depends wildly on the species and how they think.
It is possible that the Reapers used some kind of Collectors before making them to start harvesting species or to finish the harvest.
It is also possible many species lie in sleeping pods buried deep underground as their final resting place because they too wanted to do something like the Protheans but ultimately they failed. And cycle after cycles they were uncovered and then erased. And they might also have survived but not in sufficient number for their species to live on and/or the tales of the ones that survived the Cycle became some kind of legends no one in their descendants believed and thus the Cycle took place.
Because yeah it's nice to say "they'd prepare themselves" and all but... 50 thousand years would pass... They might start some highly disciplines war focused species but do you see humans stick to such way of thinking if it is not in their nature ? Plus they might become kinda like the Protheans, an empire doomed to fail.
Now crazy thought if there were always some survivors in the Cycles, just enough to uplift a couple species before disappearring ? What if the Reapers actually never failed a Cycle because they made sure the cycle would evolve as intended using former species to that end (wich they kinda already did with Collectors). Or it's actually the same species being harvested over and over again but with only the dominant species (or the one that intrigue them the most or whatever) being completly harvested with some kind of alternating evolution between some species like Humans, Asari, Turian and Salarian on one cycle, the next Krogan (Salarians uplifted them that's why I'm putting them here) and the Yahg on the other. And because they are beating back species to the dark age there is only some tales left of their harvesting.