Replace gas tank and sending unit or not?

My gas gauge reads empty, then I fill it until the pump clicks off, and by then it overflows. It only takes about 6 gallons from empty until full. I know that it holds more than that. Maybe there is really half of tank left when the gauge reads as empty. I'm almost certain this is a problem with the sending unit correct? Could the current one be fixed or is a new one the solution?

Also, would you guys recommend replacing the gas tank if I am going to rebuild the engine? I just didn't want any crap that might be in the tank to get into all the new stuff. I know the fuel filter is there but wanted opinions. The original tank looks good other than some light surface rust.