The best kind of batteries to put in a mod are LiMN, LifePO4, or protected Li-Ion, in that order.
Batteries labeled with "AW IMR" before the number are LiMN. For example, the AW IMR14500. But, not all battery sizes come in LiMN versions. For example, there is no LiMN 17670 battery.
I believe LifePO4's are labeled as such.
In terms of protected Li-Ion batteries, AW is very well-liked, and I tend to go with that just because it has such a following.
Never use unprotected batteries, and while lots of people do stack with no problems, it does increase the risk of failure. How much, I'm not sure, and it's probably not so bad if you're using safer batteries. But I won't do it when I get my mod. Just not worth worrying over it to me. If I want a stronger vape, I'll slap on an LR.