I've been using Powerizer RCR 123a in my BP since I got it and really surprised by them, (probably the best price vs runtime ratio of them all) they aren't protected though which is fine in the BP but might not be recommended for use in another mod. AW has been tested with it and have very close runtimes and are excellent quality batteries.
Protection is built into the mod so you can use either protected or or high drain with it. I'd personally go high drain unless you're going to be using the same batteries in another mod then I'd go protected that way your covered if your other mod doesn't have the protection that the BP does built into it.
As far as size any 16340 or RCR123a will work. Some batteries in those sizes available are 3.0-3.2 volt, you don't want those, stick with 3.7v. I'd personally recommend Powerizers or AW although Ultra and Trustfire is popular and will work fine.
The charger they sell with it a TR-001 is fine and will charge many different size 3.7v batteries. It does have overcharge protection but some reports say it continues to trickle charge at the end of the cycle (which I can't confirm) and shouldn't be an issue if you remove the batteries soon after they are done charging. I use a WF-188 which is versitle with sizes, charging rate, voltage selection and doesn't trickle charge. I haven't had any issues with it, there are MANY choices available though. If you're shopping around for a separate charger you want overcharge protection(which most have), doesn't trickle charge and will charge a variety of sizes so you'll be covered with any future mod batteries you might want to use with it.
Here's some battery comparisons in the Buzz Pro that you might want to check out.
http://www.youtube.com/watch?v=M6USIvOUVsw
