There is a simple select/unselect box which you can use and google will backup and restore your apps and *some* settings when you switch device. you simply have to sign on using the same gmail account. look for this option in the settings category. this can be done irrespective of the device brand. this will automate reinstallation of previously used apps.
lets say you get a major brand (sony, htc, motorola,samsung etc). they typically include backup/restore functionality on the device without using third party app. in addition they also provide PC software that can also handle your backup restore.
the benefit of using a simple app from play store is that, it frees you from using a pc to restore.
regarding home screen shortcuts, as you know there are many "launchers" on android. if you goto the settings of that launcher, you can easily restore app shortcuts and everything else for that launcher. so you have to use the same launcher in the new device if you want to have it restored.
https://play.google.com/store/apps/details?id=com.jrummy.app.manager
try Jrummy's "ultimate backup pro" (free and paid $1.50 app). excellent utility. rooting is NOT required but if it is, you get some additional features. this could handle many things you've mentioned.