A cap is basically a band-aid on cancer.
It'll work for a while, but in the end the battery & alt will suffer...especially if you plan on cranking it up all the time.
I'd suggest the "Big 3" as others have.
Find a 200a + alt if you can, you'll be glad you did someday when you want to add another amp, lights, etc.
While upgrading the alt, definitely upgrade the wimpy stock wiring. You can add a 300a alt, but if the power can't get from the alt to the battery/system, you've really not accomplished anything.
Don't forget: the ground is just as important as the power wires. Ground engine to frame, frame to body, body to battery.... every ground wire should be the same gauge & likewise the same gauge as the power wire.
The extra battery would be beneficial if you plan on cranking the stereo with the engine Off, but you'll need a battery isolator/switch for proper charging. I'm sure some of the most experienced electrical guru's here can suggest the proper equipment if you go that route.