Using LiFePO4 for a back-up solution would have my votes a hundred times compared to Li-ion (there were other threads about this.) They are much safer, can take a lot of beating, and are rated for a much greater number of charge cycles. Downside is, of course, a lower energy density.
The charging process is very similar to that of a Li-ion, only the voltages are different. There are many charging ICs you can use to charge LiFePO4 batteries. But yes, they are a lot more forgiving than Li-ion ones.
I read the datasheet of the one you linked, and it is unclear from it if it does embed a protection circuit or not. But it does list a number of safety tests showing that it can handle pretty severe beating with no adverse effect. I'd actually be surprised if it didn't embed a PCM; Li-ion batteries of the same format do. (It's a small circular PCB right beneath the + pole.) If in doubt, you can ask the manufacturer.