How to calculate how much energy a circuit wiill use, to find the appropriate battery
Get your circuit working and then turn off the power. Put your meter into current mode; the 200 mA scale is probably sufficient.  Put your meter in series with your circuit by attaching the red lead of meter to the power supply, the black lead of meter to the input of your circuit, and the negative lead of your circuit to the power supply's negative terminal. Apply power; you will see the actual current usage of your circuit. Without circuit details I can't know the consumption, but I bet it will be 50 mA or less.  Watch it as you operate all of the circuit's functions to see if the demand changes with different activities.

When you choose a battery or power regulator for your circuit, make sure it's rated higher than the minimum to account for surge at power-on and other power spikes.  500 mA would probably be good enough for a circuit like yours, but that's just a guess.

There are all kinds of complexities that can change things; if you are using motors, power consumption can go much higher than when the circuit is still, and there are other issues.  But that is too complex for this conversation.