What's holding me back is what I read about batteries, how fragile they are and how they self destruct if you don't keep them plugged in all the time. Is this still true?
Individual cells are usually fragile (as in, you can dent or puncture easily). However, they are usually protected by their enclosure.
If you are talking about lithium cells, then you should not drain them completely. Which means that they should be kept with some charge. But, unless you intend to keep them stored away for months at a time (and maybe even then) you should be fine.
There's also that fact that, when people think about batteries, they think about laptop batteries. Those are optimized for power density above all else. They are not the only type of cells available.
If you are worried about safety (and charging cycles), get a LiFePo battery (https://en.wikipedia.org/wiki/Lithium_iron_phosphate_battery). This is the same kind usually found in electric vehicles and hybrids.