Hi dogcow (LOL @ name). Safe
batteries will be those that have internal built in protection circuits or are a safe chemistry. You can learn more about batteries for mods here
http://www.e-cigarette-forum.com/fo...9007-warning-rechargeable-batteries-mods.html.
A battery that will last the entire day would be the 18650 or larger battery. This of course, means a larger mod. The mAh (milli-Amp hours) rating of the battery is what determines the length of time you will be vaping between charges.
Mods that would be compatible with your KR808D-1 cartos would be
any of them... As long as you get an adapter to fit the original model fitting of the battery mod you buy.
For example, the Darwin (with a 510 fitting, which I have) would be able to run your KR808D-1 cartomizers with a 510 to KR808D-1 adapter. Several suppliers have them. The best prices I've seen are at Goodprophets.
PV Adapters
You'll need to decide shape, battery size, and if you desire a variable voltage mod or one with a regulator in it (to keep the voltage up without drop off). Reading the reviews is a good thing. They all have their plus and minus features. You can find reviews here
http://www.e-cigarette-forum.com/forum/e-cigarette-mods/ and here
http://www.e-cigarette-forum.com/forum/e-cigarette-video-reviews/