Powering Arduino and Pump with One Battery

Hello, I could use some advice on powering an Arduino nano and a small 3v pump for a project where I only want to use one battery circuit if possible. I was thinking either a 1S LiPo, or 4 AA batteries to power both items.

For the 1S LiPo Scenario:
I would need a boost converter for the Arduino, but due to the pump being rated at 3v would I need any extra electronics other than a direct hookup to the battery with the switching? Would there be an issue with sharing the same circuit even when the Arduino is hooked up through the boost converter?

For 4 AA batteries:
I would need a buck converter similar to this one to step down voltage and power both the Arduino as well as the motor. Would I need to wire two separate buck converters in order for this to work (one for the Arduino and the other for the motor), and would the same issue potentially arise from being on the same circuit?

If anything, I just would like a little more insight as to how to power an Arduino and motor/high power accessory using the same battery

The pump is rated at 0.18 Amperes, but the starting current will be 1 to 2 Amperes. Did you notice that it is not designed for continuous duty?

What is the required battery lifetime? Lithium based batteries MUST be charged with the proper charger, and MUST NOT be discharged past a certain limit, or they will be destroyed.

You will need a suitable transistor switch or motor controller to handle the pump.

Motors generate lots of disruptive or damaging electrical noise and any single power system must be well filtered to handle both an Arduino and a pump.

Yes, I am aware the pump is not designed for continuous duty. I will be using it to water a plant 1-2 times day, so the pump will maybe be on 30 seconds at most a day. As for battery lifetime, with a 1S Lipo I would like to get as much time possible, but I should just be able to order the specific mAh capacity I need as long as the consensus is that a single cell LiPo is a decent way to go. Same goes for the couple AA batteries scenario. If I go the LiPo route, I would implement a charge controller similar to this. I am pretty sure implementing something like that is pretty straightforward, but I need the insight on how to make sure my Arduino is protected on the same battery with some potential avenues to look into in terms of wiring that sort of setup.

Attached below is how I have my pump wired up (in place of the motor) without the capacitor between the motor leads. Currently it is just hooked to a 9v battery for testing, and it works. However, from the research I have done already, a 9v is not the way to go especially if I am powering both off of the same power source.

TIP120 with motor.jpg