You should really build or buy a real PC for mission critical operations like this. The Intel NUCs are widely known to be very underpowered. Honestly, this all comes down to your budget, though. How many machines are you going to need? Do you need them to be pre-assembled?
Another thing to note is that web browsers like Chrome, when you never restart them, will continually use up more resources, so its not just processing power you need but a good amount of decent RAM as well. Windows isn t the best choice of OS for running 24/7, but in my experience Windows 7 was the most stable, and definitely lighter than Windows 10. The problem is that Microsoft is dropping support for Windows 7 in January, 2020, so if you are using Windows 7 right now then you ll also have to figure in more processing power and RAM just to keep Windows 10 running smoothly.
Personally, I d go with a late gen Intel i3 processor, stay away from the Celerons or Pentium branded CPUs. For example, the Intel 8100 or 9100 cost about $120, and are rock solid for stability, 4 processing cores which Chrome will make the most of. (Make sure not to get one that has the F suffix, as it does not have integrated graphics so you d have to provide a GPU). The maximum amount of power it will use is 65 watts, so it s not incredibly power hungry like a high end desktop, but definitely more than the little low-power Celeron unit you have right now. It ll cost more to operate, so if you have loads of these boxes, maybe that won t work for you. The trade-off is that the low power budget processors like the one you have will never be as reliable, since they are made for mobile computing and non-critical applications.
I d also go with at least 16 GB of RAM, which will make sure that your system doesn t get overloaded by Windows and Chrome memory bloat. If you have to skimp on RAM, do not go less than 8 GB. There are many cheap PCs offered that only have 4GB of RAM, this is not enough to properly run Windows 10 with memory hungry applications like Chrome and Google Earth well for 24/7.
For storage, small 64 GB SSD will suffice if you don t download anything or need any other software installed on it, and they are dirt cheap right now, any brand will suffice since you re not looking for performance out of your storage.
If you need to buy something pre-assembled, this will give you an idea of what you re looking for, however if you get the parts yourself you can definitely build something cheaper than this. At $370, you can get this HP machine with Windows 10 already installed: https://www.newegg.com/acer-aspire-t-tc-865-neselecti3-student-home-office/p/N82E16883101686