Everyone needs a hardness tester.

[tonyfoale]

Searched (Ctrl+F) your PDF for which version Arduino Nano chosen best suited for this tester. There are many choices, bewildering to newbs......such as 67AH8870. Remaining bill of materials very simple, resistors etc are clearly self identified. The video, and schematics make this a slam-dunk to re-create, not intimidating at all.

Almost any Arduino will do. I use the Nano because it is so small and easy to fit in boxes and on to circuit boards. As shown in the video I use an Arduino Uno (which as the name suggests was the first) for development or proof of concept work, its larger size is better for that. Otherwise the Nano is the same.
I think that all the Arduinos fit into one of two classes.
1. Genuine
2. Clones.

The clones are legit because the Arduino hardware is open source, however there is a difference. The genuine ones use a comms chip for which they have to pay royalties. To keep the price down the clones use a royalty free chip which needs a software driver. This is a free download from many sources, look for the English version (unless you understand chinese) of the CH340 driver. This driver is to allow the inter-connection of PC and Arduino via a USB cable, which is simpler than an alternative method of serial communication.
On the net there are many complaints by people who cannot get a clone to work. All or the vast majority that I have seen are due to the complainer not following instructions to get the driver. It is just like loading any other hardware driver into a PC.
This driver is only needed for communications between a PC and Arduino for either programming the Arduino or for applications where you run the Arduino in conjunction with a PC.

As for which Nano to use, I would say ANY. The cheapest require you to solder on the supplied header pins so if you want to avoid that, look for those that come pre-fitted. You may find it useful to look up adafruit.com, they are a company which specialise in electronic hobby stuff and have their own range of many variants of the Arduino and they have loads of free download help and tutorial files. I do not recall ever buying from them but they have built a good reputation. They are in NYC.
https://www.arduino.cc is the official Arduino site and is full of help files, programme examples and forums etc.

Just to make the process clear.
An Arduino can operate autonomously or it can run connected to other stuff like a PC or even other Arduinos.
The programming is usually done on a personal computer and then downloaded to the Arduino via a USB cable.
You need to install the Arduino IDE (free programming software from the Arduino web site) then you write your programme (for some reason they call a programme a sketch, I don't) or in this case you copy and paste the programme that I listed into the IDE and then download to the Arduino.
If it is a stand alone application you can then disconnect from the PC and feed the Arduino from a battery or wall wart etc.
Some applications like data acquisition will need to keep the PC connection to download data. The connection in some cases might be two way, you might use PC software to send commands to the Arduino.