We have a Floppy Seat and we love it. http://www.babyearth.com/floppy-seat-ez-carry-floppy-seat.html?att_val=5712&utm_source=google&utm_medium=cpc&utm_term=&kwid=productads-sku^18678@ADL45712-adtype^PLA-adid^17784673123
It's cushioned/padded and it folds into itself for storage. It stretches enough to fit those big Costco carts. We also use it at restaurants in their high chairs. The padding came in handy when baby sort of leaned to the side at first. lol It also has loops for her toys, and a pocket for her bottle.
I thought I'd have an issue with bringing it around, but I leave it in the trunk so it's always with me. The trick is to install it into the cart before you take baby out of the car.
As far as germs, we forgot to bring it once, and used the restaurant high chair...flies started swarming around the high chair! Ewww...from then on, we have always used it.