I realistically only really need 9v, that being said I have looked at those kind of batteries but the problem arises when I need to charge the battery. It has to be charged through a micro usb (part of the challenge) and the batteries I have come across use a special kind of charger, using a device like the dc to dc converter with the micro usb saves me time, money, and patience.

People often think that the design of an SMPS (Switched Mode Power Supply) is an easy task. I assure you it is not. I got my degree in Electrical Engineering 50 years ago. I have done a couple of designs. Getting to high efficiencies is a little bit like designing a spaceship fro travel at light speed. The closer you get to perfection the harder it is to make even slight improvements. Every time I do a design I learn new subtleties that never previously came up. I consider myself minimally competent to do a design that works. It is far more likely that you can find a product that is appropriate to your needs with diligent research and skeptical eye to advertising claims.

 

The battery I want to use is attached below

 

The alternative to all of this would be to do what you said and just buy a DC car battery, but the thing is I wouldnt know how to hook it up to a micro USB to charge the battery while also having it connected to and powering the rest of the circuit.