Fuses/Breakers

Fuse/breaker size is primarily determined by the safe current carrying capacity of the wire after it. They're there to prevent fire in the event of some catastrophic problem (like a short to ground).

For the 10 AWG solar controller wire, 30A would be reasonable, as close to the battery as practical. From a voltage drop perspective, a heavier wire may be beneficial here.

For the 4 AWG wire to the inverter, 100A might be appropriate, and probably a slow-blow fuse or thermal curve circuit breaker would be most appropriate. This wire seems rather marginally sized for a full 1000W load from the inverter.

For a catastrophic fuse at the battery, that depends on the details of what is connected and how it's connected and what your maximum possible current draw is. On my motorhome I believe it came with a 175A fuse there (and I think 2 gauge wiring for the battery post connections). The only time such a high current could possibly be expected is when starting the generator or the main engine with the emergency start switch pressed.

On a trailer, my general understanding is that the connection to the breakaway switch (and thence to the trailer brakes) should not be fused. I do not claim to be an expert, nor did I sleep at Holiday Inn last night.

DrewE wrote:
For the 4 AWG wire to the inverter, 100A might be appropriate, and probably a slow-blow fuse or thermal curve circuit breaker would be most appropriate. This wire seems rather marginally sized for a full 1000W load from the inverter.

The OP hasn't indicated how long his battery > inverter cable runs are so it's difficult to say whether 4 gauge was appropriate. When I installed my own 1000 watt inverter in our trailer's front pass through storage compartment I required 6' cables to reach the battery so I used 4 gauge cables which this Blue Sea DC Wire Gauge Chart indicates as suitable for my intended maximum load of 70 amps. I wired it in using an 80 amp fuse and it's worked out just fine.

Inverter and controller are 3 feet from the battery.
4 AWG works fine for my present loads.
Connections on the battery are controller, inverter, and trailer main.
Read somewhere to connect controller to inverter leads. Pros and cons?
Should I be using a buss bar?

In terms of how things will work electrically, it doesn't make a lot of difference how they get connected (within reason).

In terms of practical mechanical matters, it's easier to connect only one or two wires to a battery terminal than try to manage a plethora of them, and there's much less of a chance for something to work loose or make a poor connection in the middle of the pile. A buss bar is a nice solution to that. Typically the master fuse would be somewhere betwixt the battery and the buss bar.

Good info, thx