Ken...
Real quick and to be clear... I won't be of help on the subject of the quad or it's use etc... I only have experience with airplanes... I also may know other technical stuff as well... but nothing multicopter etc.
As for batteries, lets talk a little about safety... I do have some experience with certain types including Lipo's like we use in the RC hobby. Lipo's are a particularly volatile type of battery and should NEVER be charged unattended or for longer than it takes to reach a full charge. In fact, it's highly recommended to charge them within a fire safe location in the event that they catch fire, typically or at least many times it can be explosive or nearly so.
Once fully charged, you should use them within a few days and if it'll be longer, drain them back to their storage voltage which is around 3.6v-3.7v. Keeping a full charge in them is hard on them and shortens their life expectancy. On the other side, you shouldn't drain them lower than around 3.3v-3.4v as well for much the same reason, so after a flight, charge them back to their storage charge if you aren't going to use them immediately.
When storing your batteries, again store them in a fireproof storage container. Don't place them near anything else that may be flammable such as wood structures or any that may catch fire in the event that something catastrophic does happen. If you happen to have a crash with an electric vehicle, separate that battery from any others you own ( after getting it back to a storage charge ) and keep it also in a fireproof container.
As for other battery types, find out what their recommended care and use instructions are. If you are unaware of what they are, certainly don't leave them on a charger. Always supervise your batteries of any type while charging them. Do not leave them unattended unless you've read instructions that specifically says it's safe to do so.
All batteries have a risk because they store electricity in a condensed manner. Lipo's are some on the most dense electrical storage for their weight and size which is what makes them good for this type of use but also is why there is a higher risk of having a problem. When a battery is in a crash and the membrane between the anode and cathode is compromised, it can set off an uncontrollable chain reaction resulting in the release of all of the electricity at once causing a fire. Also if they aren't cared for like I mentioned for charging/discharging or overcharging, it can cause dendrite crystals to start growing in them which in turn can again breach the membrane I mentioned... and again it can start an uncontrollable fire from the electrical discharge.
Most of the time... as long as you take the proper safety precautions... you are unlikely to have a problem but it's certainly possible and I personally know of two hobbyists that had it happen. One of them had their garage damaged and another lost their home to a fire. I've even had an airplane right after a violent crash catch fire.
If you think I may be over stating the potential risks... do a Youtube search for "Lipo fire" for many examples of controlled instances of it happening and how violent it can be.
Oh... one last thing... this is about learning about each type of rechargeable battery and how they can differ. Some batteries are better off when stored to have a trickle charger on them... Like lead acid batteries and I believe ( not certain ) that nicads also prefer a trickle charge. In any case, check what the recommended steps for the type of battery you choose to use for anything so you can get the most out of them and also be as safe as you can be.