"Li-ion" and "Li-Poly" are both the same chemistry (LiCoO2) - the only difference between them is that lion typically refers to packaged round cells while lipos usually refer to flat pouches. LiFePO4 is literally a "lithium ion battery" (so is NMC) but has very different properties - energy density is almost half of the lithium-cobalt, but they are much safer and more durable and are used frequently for buses and for off-grid power.
Capacity is meaningful, but as you mention there's a lot of questionable claims and counterfeits. Also if you are using pulls, of course you need to do your own testing (the least safe part of what a lot of DIYers are doing). It's not that hard to get good batteries however. First, you make sure that you have a proper spec sheet, or barring/in addition to that, have thoroughly tested models. Then order from a reputable dealer that tests every batch of batteries they receive. Options might include BatteryBro, Liion Wholesale, or IMR Batteries. I've ordered batteries from the latter two. You'll still want to do your own testing.
If you are brave you can DIY your own spot welder pretty cheap. SUNKKO S788H's are <$150 and will get the job done.
This is wrong on many levels. Firstly, if you want UPS software that is open source, NUTS has been around for years and can easily talk to many COTS UPSs.
If you are just building a battery powered PC and want battery reporting, all you need to do is to makes sure you are reporting voltage (all capacity is based on profiling voltage curves for batteries, all limits on battery health are based on battery voltage as well btw) into your computer. What you need is a simple ADC and resistive voltage divider. Here's a very good tutorial on how this works. For a more plug and play solution, you can use something like this and only worry about proper resistors to divide voltage.
One other note, when you are building your own battery packs you want to consider continuous amperage, which is a separate rating/characteristic of a cell from capacity (you typically trade one for the other). There are other considerations like ESR/internal resistance but not as big a deal for batteries.
Your easiest solution is to use a $20 Y-PWR board and 2 x $80 5S1P 8000mAh lipos. If you're lazy, pick up some low voltage alarms and call it a day, otherwise you can find some tutorials on building ways to communicate voltage via (see above) GPIO (if you don't have access to GPIO on your system, I've used this Numato USB GPIO module before that works pretty well).
As far as charging, if you aren't using a BMS (you probably should) then you can use something like this Q6 Plus, although you might want a dual charger if you're going to have two of those lipos.
If you're up for doing a little more work, you can build your own battery out of standard cells w/o spot welding with something like the Vruzend system. Makes it dead simple to build any size of battery you want. Since it's not very high amperage, you can use really any random cheapie BMS board if you want to simplify your charging requirements.
