16GB is nearly not enough space too, so the low end iphones are useless.
Apple is very inefficient with storage space with streaming services. I put almost no photos or media on my device and it fills up with streaming cache that you can't clear in many instances, you have to delete and reinstall the app to clear that memory. Happens quite a bit with my google music streaming, Sirius XM, etc.
Are you able to easily stream shit you got in the Apple Store too? It sucks on my ipad and I have like 100MBPs internet, apple TV is fine. Just puts way too much in the cache and eventually fucks it all up.