So i just bought my 2006 winning blue mazda 3 hatch... I wanna installed my sound system to my car... I currently owned a 1k amp, 1k, subwoofer, with the other wires... I know i will need to do the big 3... will that complete it? Or will i need a new battery and a better alternator?

 

what is a 1k amp, 1k sub!
What size fuses are on amp?

 

ahaha my bad... 1000 watt apmplifier, 1000 watt subwoofer... my fuse on my amplifier is 30/30 dual channel... but i only use 1 subwoofer.... I crank the bass few times a day, but not alot... so will i need a stronger battery or alternator?

 

Your fuse sizes aren't bad. I have a 600 watt mono and it has 4 20 amp fuses. I don't have a bigger alternator and i do crank it sometimes more than not. If you are only using 1 side for 30 amps you will be fine.
I do have a better battery but only change it if you are having issues. Then get a flat plate agm type and try to get a little bigger if you can, if it'll fit. And wrap it in insulation to prevent the heat from the engine killing it and also keeping in warm in the winter!
Biggest issue is get the largest power wire you can for best bass response. I had my amp way in the back and my wire not big enough. I moved it up behind the front seat and now have bass.
You should also add an extra ground wire from negative terminal to the body somewhere as you should not rely on stock ground since you're only grounding close by where you install your amp.---it completes circuit better. Another ground wire to engine block will also help with your pumping alternator. I also have a fuse/breaker just by the battery positive terminal which really helps if you get t-boned.
I also have a cooling fan on my amp since inside car temps can get quite hot.