As already pointed out in above comments, there are multiple questions on this site offering parts of the solution you might need:
I'd recommend you taking the payed version of the last mentioned app. While 5 bucks may sound a lot in terms of an Android app, you won't ever regret having spend them. TiBu was one of the first apps I've bought years ago, and I'm still a happy user. Using this app, you not only can backup all your apps including their data, but all your messages, contacts, call logs, and whatsnots. Even the system settings go along. Provided you get back the very same device running the very same Android version, you simply can go ahead and batch-restore everything (Pro only; with the free version, you need to do this manually for each item).
But even if you switch to a different device or Android version: restoring your apps+data goes the very same. Just with system apps and their data (including your APNs, WiFi hotspots, contacts, text messages, etc.) you need to take special care. TiBu offers a "migration mode", which I strongly recommend in that case; but still, some extra care cannot hurt: For your user apps+data, use the batch mode -- no problems to expect there. But for the just mentioned system stuff, better restore items one-by-one using the migration mode, and then check if everything works fine (even a reboot in between might be required, e.g. after restoring your text messages, contacts, and the like, as Android does not expect them coming that way). It's just in case. And if something seems "botched", remember what you restored last -- then do a factory-reset, batch-restore all apps, restore everything up to the point before the "botched" item, and skip to the next.
I don't expect any trouble that way. But in case it comes (thanks to Murphy's Law), you're welcome to ask that in a new question, giving the details, and we'll do our best to help you again.