No, you don't need an airstone - especially if you have live plants. Do you have chain stores like Petco and Petsmart where you are?
If you buy a kit like the one pictured here, it comes with the filter, light hood, & thermometer already. Then you would only need a heater, gravel, decorations, and plants to get started.
I'd also pick up a better water conditioner like Seachem Prime or API Stress Coat to use with water changes.