Your cell phone only has 4 GB of memory, you can get it fairly clean, but in no time you will get the same trouble again, it just doesn't have sufficient memory. try getting one with 16 GB.
I disagree that 4G is necessarily too little.
The key is to understand that a phone is not a place for the PERMANENT STORAGE of stuff (especially media files, such as photos and especially videos) whether taken with the phone or send to the user by others. The idea is to periodically transfer photos and videos elsewhere and delete them from the phone.
Of course, if the phone accepts memory card, why not? they aren't that expensive these days.
A new phone may not be necessary, depending on the users needs. If it is just calls, text messaging, simple web browsing, social networks, and occasional pics and videos, any reasonably recent phone may be OK. Keep in mind that a new/expensive phone can be lost/broken/stolen at any time, sending the user back to the store.