May I ask why you're using mp4s for audio? Mp4 is typically used for video/multi media, where mp3 is purely for audio and has a far greater number of applications that work with it. (And there are plenty of web sites that can rip the audio out of a YouTube video and save it as an mp3). Any site that converts YouTube to mp4 is probably including the video portion as well. If all you're after is the audio, use a site that converts YouTube to mp3 instead. The files will be audio only, and considerably smaller file size, and there are a lot more mp3 player apps out there than mp4.
In any case, that choice is yours, and no matter what you choose, you'll still need to get the files over to your phone one way or another.
The difference here is that if you use YouTube or Google Play Music for streaming, you'll have to transfer the audio information every time you play a given song, but if you transfer the actual file, you'll only have to do it once and then you can play it locally from then on. (Yes, Google Play does have the ability to play local content, but there are tons of other mp3 players as well, so pick the one you like the best)
So, how do you get files to your phone?
The easiest way is just to plug your phone in to you computer via USB. Assuming you're on a Windows box, it should show up as a Multi Media Device or something similar under My Computer. Then, you should just be able to open it and drag files to it like you would any other removable drive.
Note: It doesn't matter where on the phone you store your audio files. The Android media service will check the whole contents of the phone and add any files it finds to the library regardless of where it finds them. (With the exception of notification sounds and ringtones, which have to be in one of a couple specific places).
I find the USB cable approach to be a bit annoying, so I'd recommend one of the following:
Cloud Transfers- use Dropbox/Box/Copy/SugarSync/OneDrive/etc. Sign up for a free account at the service of your choice. Install the Windows client on your computer and the Android client on your phone. Use your computer to copy the files you want up to the cloud service and then use the phone client app to copy them down to your phone.
AirDroid- This works best if you can get your phone on the same network that your PC is on, but it isn't strictly necessary. Open AirDroid on your phone. On you computer, go to the URL that your phone gives you. This will allow you to open a pseudo file browser on your computer that points to your phone's file system. Just click Upload and drag/drop your files over and they'll begin copying.
Both options work best if you can get your phone on some sort of wifi (be it yours or a public hot spot), but they'll work over 3/4g as well.
