There is a lot to try to keep in mind when you first switch to lipo power, but they are still the lightest power supply available to provide us with the burst amperages we need to fly. They are also safe when treated with a modicum of respect, and can have long productive lives when used properly.
First thing to consider is charging. Lipo's need to be charged with a reliable balance charger to maintain the balance of voltage across all the cells in a pack. If you always charge with a balance charger, risk of fire or a pack detonating is reduced almost to zero, but NEVER charge unattended! All it would take is a charger or pack malfunction, and the house goes up in smoke. Always babysit those charging batteries like they are the neighborhood pyromaniac with matches in a gas station.
If you see any damage to a pack from a crash or they puff, pay special attention to them as they will most likely be the one that fails. Usually, it's best to just write off the pack and be safe. If you do have a suspect pack, you can safely discharge it by immersion in saltwater for a few days to a week.
Next thing to consider is the power draw of your system. We talk of headroom. All that means is having a buffer or running a system that is lower than max draw from the battery. Say you have a 2200mAh 30C battery like you mentioned above. Let's take a look at what you can expect from it.
Usable capacity: this is what the battery can supply in time and power and is considered 80% of rated capacity. With your 2200 mAh battery this means you should have 1760mAh of useable power. 2200 x 80%=1760
Now this can either give you 1.76 amps for an hour or about 10 amps for about 10 minutes. How do you get that? Milliamps are 1000 per amp so 1760mAh=1.76Ah or amp hours so if you take the hour amp rate and multiply it times 6, you'll get a 10 minute amp draw.
Another thing to consider and a more accurate gauge of when to stop flying is voltage. Lipo cells have a nominal voltage of 3.7 v per cell and if you aren't flying for a few weeks, your batts should be charged or discharged to that voltage. When flying, it's a good idea to stay above 3.3v per cell but down to 3.0 volts can be done but just keep in mind that when a lipo drops close to 3V per cell, it's also very close to damage. 2.7V per cell is completely dead and lipos have a sharp drop-off, or when they are close to dead, they drop in voltage quickly! So most people set up any alarms for 3.3 to 3.7 depending on draw of the system. Also keep in mind, these voltages are per cell, so with a 3S or 3 cell battery, you need to fly no lower than 9.9 volts for the pack.
So back to amp draw. Like you said earlier, 2200 30C pack can provide 66amps of current but if you are using all of that 66amps, you'll have less than 2 minutes of flight time. It should be spectacular but short! So if you plan on just going to the max on the "C" rating, you'll also shorten the battery lifespan as they don't care for maxing out in any aspect. Main thing to consider is that your C rating can supply what you expect the max draw to be plus whatever you think is a good buffer, I usually try to have at least 10-20% of wiggle room. So I would use that battery with a max planned draw of around 40-45 amps. Keeps me well within the limits and also keep the battery cool but not pushing it to it's limits.
Hopefully this helps and I haven't completely confused you. Let me know if anything needs more clarification...
