I have a resonably nice camera, a Fuji X-T1 mirrorless. Came with the standard single battery. Anyone who actually uses their camera knows that one battery is not enough. So you buy extras. Rotate them through the camera and charger. The price of an actual Fuji Li-ion battery was $65. WAY too...
Unless you live in GB it's cheaper to get battery's stateside. (They are all from china anyway).
I have purchased many laptop batterys on E-Bay that have all worked great. Just look at their customer reviews.
That will tell you what you need to know. Save your money, and buy off Ebay.
If your not in a rush, you can run off just the power supply, and get the battery from china even cheaper.
Thats what I do. (unless it's a customers, and they want it faster, then I buy stateside.)
I just took a look at your E-Bay link. Buy with confidence. It's Original HP battery, just less cost from other sellers. HP would not sell a different chemistry battery with a higher voltage, which is the only thing that could harm your computer. The higher Amp/Hr rating simply means it will last longer on a charge.