Yep, will be using 4/0 from inverter to bus bar and 4/0 from battery to bus bar, fusing down to 250, to prevent the bms from kicking in.Your fuse should be sized to protect the cable you are using (i.e. not above the rating for the wire/cable), then if lower, for the device.
The fuse is to prevent your wire from overheating and starting a fire. Individual loads should have fuses appropriate for their wire.
You can of course use smaller fuses, but never put a fuse on that is larger than what your wire can carry.