Pandora is the oldest music streaming service. It has three types of membership. The first one is Pandora Free which is totally free for listening to, but the con is ads are embedded in this version. The second one is Pandora Plus which costs $4.99/month, you can replay music tracks and get higher sound quality. The third one is Pandora Premium which costs $9.99/month, you can download music and listen to it offline in this version.
Apple Music is newer, but compared with Pandora, it has more 5 million more songs than Pandora. It don't have any free version, but a three-month free trial. You have to pay $9.99/month after it expired. Or you can choose $14.99/month for family and $4.99/month for students.
If you are an iPhone user, I will suggest you Apple Music, for its ecosystem. If you are an Android user, Pandora is a better choice, though Apple Music can be downloaded on Android phone now. If you are a student or a part of your family, then you can choose more cost-effective Apple meals. If you just want to listen to free music, YouTube is a good platform that you can turn to. Here is a tutorial I found for how to download music from YouTube. Hope it a help.