which battery to choose ?

Hello,
I have a year-end project and the idea is to make a wireless voltmeter. We have the ideas and we will communicate the voltage by Bluetooth. The only problem we have is to find a battery to power the arduino uno and a Bluetooth module HC-08. Could you advise me a battery that would supply everything? Thank you for your help

The working voltage of the HC-08 is 2.0V-3.6V DC. If your Arduino is a 3.3V Pro Mini model it'll do perfectly fine at 2.4-5.5V, the 2.4V being the minimum voltage specification for an 8 MHz clock. So the 2.5-3.2V of a pair of alkaline batteries would work, or a nominal 3.2V (2.5-3.6V) LiFePO4 one.

2x NiMH may also work, most of the time they give about 2.4V, but it's borderline for the Arduino. Reducing the clock speed to 3.6864 MHz (that's a standard crystal value) would be fantastic in that case, great for UART communication (with the HC-08) and your ATmega328p will work down to 1.8V.

Now find out how much current your project will take, how long it's supposed to run on a charge, and you know the required capacity.

Assuming you already have the Uno, you might consider a 5v phone charger using a single 18650 but, before you do that, you need to make a decision about how long the rig needs to run. These packages can be had for a couple of dollars - battery extra. Note that I found that one of my batteries was about 1.5mm longer than usual and would not fit.

Seeing the year has nearly ended, if you just want to prove the point, and don't care how long it runs, a 9v PP3 will probably suffice.