The plan required to get the iPhone 4 free requires a data subscription. That's the point. You can't get the phone free and subscribe to data later. The only way to get an iPhone without having to subscribe to a data plan is to buy an unlocked phone, making the entry price for the 4 $450.
The iPhone 4 only has 8GB of storage.
I honestly don't know what "music specs" you're looking for. As a music player, the iPhone works fine. Any model of iPhone.
The problem you're going to have is how much music you can take with you in that limited amount of storage, which also has to hold any photos or videos you take, apps you decide you want, etc. The same goes for the 4S.
The only way you're going to get higher capacity is get an iPhone 5. Those start at $199 subsidised for 16GB with a 2 year contract. The contract will probably run you arount $80 a month including data.