If it's just a stock alternator, 4 gauge will do fine. Like canaan said make sure the wire is actually true gauge tho. Ring terminals can be crimped very well on heavy gauge wire with a tool that you hit with a hammer, smashes the terminal on there.
And a fuse in that wire is pointless. There is a power source at both ends (alt and battery). If that wire shorts it WILL burn, fuse or not.
I wouldn't fuse the alt to batt +. Just make sure it is run properly and will not snag or get too hot. Wire loom will offer a little more protection, but not a lot. That wire is not fused stock anyways.
Keep the stock wires intact, just add the 4ga. Clean and sand any paint from all contacts.
4 ga i dont think will honestly allow you to run 1500 watts.. unless its like a short run, like under 6 ft, but most people need around 13-15 ft or so. I believe that only allows 90 amps to go through the wire, i use 3/0 myself just to run a sundown 1200d, its probably overkill since im only using a 5 ft run for the power, but oh well. i say run 2 ga or bigger, you may as well spend a little extra to do it right the first time. so just make sure the run is as short as possible, you dont want an extra 5 ft not getting used especilly if its only 4 ga