You can turn on your google backup (settings, backup & reset, check off "back up my data". I'm not sure exactly how long it takes for google's server to back up but it gets done eventually. Then when you get your new phone you use the same account and do google restore and it will put all the apps/apps related data onto your new phone.
I don't think it will back up user data though so you will probably have to do that manually.
Thats what I did when I had my phone repaired. I got the phone back with factory settings and I put my account back on and it gave me all my apps back to my last save point.