You don't really need that much for only a 600 watt rated amp. The average power versus time isn't even close to that. A new stock alternator will be fine, and maybe a cap to take the edge off of the transient alternator demand. A good battery is helpful though, the same properties that make a good battery supply power better also make it charge better and can sometimes be more alternator friendly.
You don't need to upgrade your alternator wiring for a stock alternator, it doesn't serve any purpose because it's already large enough for stock output (and the wire length is short).. You're interested in decent battery wiring, so your amps can get the power they want over the distance from the battery to the trunk.