I would put a fuse between the charger and battery, another between battery and inverter, simply because the impulse energy you have on-tap with those two batteries is sufficient to cause lots of really, really bad things to happen if anything should happen to the wiring or protection of your devices.
I would size the fuses to be no more than about 20% higher than the expected limit for the machine. If the charger is a 200W, then you're looking at 200W / 14.2v = 14A. Use a 20A fuse and 12awg wire... if the wire length is long, use 10awg wire, but keep the fuse near the battery.
If your inverter is rated for 1500W, you'll pull AT LEAST 1500/11.5=130A.
Notice I used 11.5v for this calculation- that's because battery voltage will sag under a heavy load, and the inverter will compensate by drawing more current. The inverter isn't 100% perfect, there's base draw of usually about a half amp (just to be on) and it's probably got 10% loss of efficiency, so figure 130+13+.5=145A range, so a 150A fuse. This won't be an ordinary plug-in type... there are automotive DC fuses that have bolt-on lugs, but another way you can do it, is use an old AC knife-switch with cartridge fuses. They're AC, and intended for higher voltage, and they may not be perfectly accurate in their 'blow' point, but they'll work, they're common, cheap, and easy.
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