The water heater is a “stopping place” for the water. Minerals and metals in the get an opportunity to come out of solution as sediment. This accumulates and is the cause of the brownish color. Yes, you can flush the tank. However, if you have not done so in the past, you must be prepared to replace or have replaced the flush valve. A flush valve that has not been used could have its sealing component degraded by heat. Water heater manufacturers recommend frequent flushing but most users are not aware of that or ignore it. I
would not recommend a sediment filter. That may keep the sediment from causing obvious problems for you but would hide the problem of sediment accumulation in the water heater. That sediment will cause excessive fuel consumption and failure of the water heater.