Your contacts will be backed up to your Google account (you can double check this by going to settings > accounts and sync > google and checking that the 'sync contacts' box is ticked.) They should also back up your app data too, but i'm not so sure how reliable it is. Unfortunately I don't know how to backup apps from a non rooted phone, sorry In theory, Google should also backup your wifi passwords and some other similar data but it's never worked for me.

If there's anything else you need let me know

 

A list of the apps that you have downloaded is available on Play (menu=>my apps) - I believe any paid apps may even start to download automatically (not 100% on that though). It would only be app data that you would loose which, as CDPlant says, I am not sure if you can back up without being rooted

 

Just found MyBackup on Google Play - https://play.google.com/store/apps/details?id=com.rerware.android.MyBackup&hl=en which says (quoted from the description)

"MyBackup and MyBackup Pro will work on all Android mobile devices, regardless if they have root access or not.
Backup (with schedule option) to our online secure servers, or SD card, your Applications, Photos, Contacts, Call log, Browser Bookmarks, SMS (text messages), MMS, Calendar, System Settings, Home Screens (including shortcut positions), Alarms, Dictionary, Music Playlists, and more"

So might be worth giving the free version a go and see if it works

 

Sounds like a most useful app