strange gas level readings

I have a 99 Buick Century that has started to give me goofy fuel readings. When I start the car it will normally read what I believe to be an accurate level of fuel. If the car sits idling for a short time it will read past empty. Sometimes it will read somewhere in between the two levels. I've heard a bad ground will do this. Others have believed it to be a bad sending unit ($260-ouch!!) Any ideas would be appreciated. Thx

Best to check the ground's to see if you have bad contact before jumping into the sending unit. You are heading in the right direction.