If I uninstall Google Play Store and Play Services will that delete files such as texts, pictures and more. My issue at hand is this error continuously appearing on my phone: "Google Play Services has stopped".
No, it would not delete your files.
You should always keep a backup of your data anyway. The error you are seeing is because these services are defined as system services and there could be some of the other background services which are are trying to access it.
Google Play store and Google Play services are system apps which require root permissions to be removed.
If you have root permissions, yes you can remove Play Store and Play Services completely and doing so will remove your google account from the device and might break other Google propreitary apps on system, if any. And no, it will not delete any texts, pictures, videos, or any files on sdcard. And if your device is on lolipop, removing Google Chrome might remove WebView and break Messaging app (it fails to open complaining about WebView). But messages are not deleted, once you restore Chrome they are back.
And if your device doesn't have root permissions, you cannot completely remove Play store and Play services as they are system apps. All You can do is to remove google account from device and uninstall updates for them. Be aware that if you don't remove Google account and uninstall updates for them, they still get autoupdated on their own. And no, uninstalling updates for play store and play services will not delete any texts, pictures, videos, or any files on sdcard. It should be safe.