Your car is fine. The gas gauge isn't 100% linear, so while it might appear to sink quickly at the beginning, it will steady out. My bugeye will drop 1/8th or more in the first 50 miles, then the needle seems to drop more slowly. Now if you suddenly see the needle drop to empty, and you find after dividing the trip meter by the gallons purchased that you're getting 12 mpg or something, then that is a legitimate cause for concern.
It sounds like you just need to get more familiar with the car, honestly. I think you'll be fine.