Are you wanting to install circuit breakers on the DC (battery) side? If so, you won't need them to protect the unit as it is already fused. But, it would be a good idea to install them as close to the battery so that if a wiring fault develops in te cable going to the inverter, it would be protected as well.
For the AC side, breakers are sized according to the wire size, not the capacity of the inverter. But, you can always use a smaller size if you want to try and protect the inverter from overloads as well. Your inverter is rated at 1000 watts, which is a bit over 8 amps of AC current. Use a 10 amp circuit breaker, and don't use smaller than 16ga wire for short distances. Use larger guage wire (12ga is 20amp residential requirement, 14ga is 15amp residential requirement) for the longer runs.
This inverter is not designed for a permanent install, its not intended to be run continuously. There are inverters designed for this, you can find an idea of product selection at rv suppliers, alternative energy shops, etc.