Yeah, that should work. Amplifiers can range a lot in price depending on features, quality and power. How much power you need depends on what wattage the speakers are and how loud you want to drive them.
Are you sure you're not just better off leaving them connected to the stereo, and connecting your audio source to that? Even if it doesn't have a 3.5mm jack, if the stereo is also a radio you can get an FM adaptor with a 3.5mm input.