If you want more than wireless audio, a portable CarPlay display can add a touch screen without replacing the factory radio, and many similar displays also support Android Auto. These are separate screens that mount on the dashboard or windshield, much like a standalone GPS unit. Your phone connects to the display, which can show maps, music, calls and messages. Depending on the model, its audio can then play through the car's existing speakers using AUX, FM or another supported connection.
One accessory won't help with an older, non-smart radio: the small USB adapters sold for wireless CarPlay or Android Auto. A wireless Android Auto adapter only works with a car that already supports wired Android Auto. It can't add the platform to a stereo that never had it. The same limitation applies to wireless CarPlay adapters, as noted in our our CarlinKit 5 review.
A permanent approach is replacing the factory stereo itself. This part of the car is often called the head unit. An aftermarket head unit takes its place in the dashboard and can add features such as a touchscreen, Bluetooth, CarPlay and Android Auto in one built-in system. The catch is that the original stereo may do more than play audio. In some cars, it's also connected to steering-wheel buttons, backup camera, factory amplifier or vehicle settings. Keeping those features working can require vehicle-specific wiring harnesses or interface adapters, so be sure to check compatibility before buying a replacement. You might need a professional to do the swap properly.
If your car already has the connectivity you want, none of those upgrades will fix mediocre audio. Better speakers can improve clarity, an amplifier can give compatible speakers more clean power and a subwoofer handles deeper bass. There are also ways to improve CarPlay's audio quality, some of which work for all the above methods.
There's no single upgrade order that works for every car. Start with the problem you can actually hear or the feature you're missing, rather than replacing components simply because they're older.