Will I be able to keep the music from my iPhone?

I have an iPhone 4S with over 100 songs on it but I have no computer and don't plan on getting one in the near future. With that being said will Verizon be able to transfer my music frommm phone to my next one (assuming its an apple product)?

Yes… They can transfer music, contacts, and everything.

If you have iCloud enabled then and log in to it on your next apple product then you'll be able to stream the music on your iCloud account