Please do not fit a standard lead/acid battery inside the car, yes i know it's the boot. To fit any battery in the boot, it still needs to be done properly, secured correctly and with protected terminals. If you are daft enough to use a lead acid type, it also needs an external vent, acid gives off toxic fumes which are not only dangerous but flammable.
If you do a job, do it properly, fit a gel battery. We use
Optima's when we do a boot install, i have a yellow top in mine.There are plenty of suppliers, shop around for the best price.
It's quite a common set-up on modified cars.
We run the cables through the car. Just make sure that the cables are protected by using correct grommets when drilling through the bulkhead, common sense tells you that you need to plan where to drill etc.
Don't run power wires the same side as audio wires.
Use a breaker and correctly rated fuses.
Done properly it is a good enhancement. Done on the cheap it is most probably dangerous and bloody awful.