Please keep in mind that the heat can be quite intense, so make sure to pack sunscreen, sunglasses, a hat, and stay hydrated!
You can arrange an airport pickup with your hotel directly if they offer that service, otherwise, the airport taxi is clean, safe, and reliable. The fare to Amman in a regular sedan should be around 22.5 JOD (~30 USD). You can refer to this website for more info (https://www.qataxi.com/en/tariffs-price).
Within Amman, you can get around easily with Uber (or our local version Careem), it is safe and reliable. Another option would be to rent a car from the airport, it will give you more flexibility, but please take care while driving in Amman during peak hours!