The brake pedal to the floor is the brake system (master cylinder, wheel cylinders or hoses). You should bleed the system, look for leaks, and replace faulty components. You won't necessarily see leaks if there are problems (internal seal leaks in the bad cylinder). If there are leaks they definitely show a problem at that location.
The stock brakes are fairly decent, especially for just normal driving and stopping. Get the system up to par and it will stop well. If you are going to do lots of performance mods you could upgrade, but it isn't needed until then.