Yeah, you're on the right track.
Understand that the fuses are to protect the wire from too much current. If too much current flows down the wire, the insulation could melt and cause a short and possibly a fire and all sorts of nastiness.
You've already figured out that the fuse at the battery should be between the max rating of the cable and the total power draw of all devices on the cable.
I'd think your 60A fuse should be fine, even with the thicker wire at the battery. If the fuse blows, replace it with an 80A fuse. I doubt it will be an issue, though.
I use a 4AWG with a 100A fuse at the battery for the PC, a small inverter and two amps.
Works like a charm and I don't fear a fire from a short-circuit.