If your phone is set to store contacts in Google/Gmail and you use Google Calendar too, then your email, calendar and contacts will re-sync when you add your google account to the new phone.
For apps, since Google Play keeps track of ALL apps you've ever installed (free and purchased), you have a couple of options... 1. Clean up your my apps list in google play, (from the my apps -> all list, you can remove those apps you no longer use), then when you sign into the google account on the new phone and open play, you can go to the my apps and install them one by one. or 2. Use something like Appbrain. Create an account or sign in using your google account, and it will sync a list of the CURRENTLY Installed apps on that phone. When you install AppBrain on the new phone, it will likely create a new list. So log into its web site, and copy all the apps from the old phone's list to the new phone's list. If AutoWeb Install is turned on for the new phone, all the apps will start installing (from google play). These two options will NOT bring your app data across.
A 3rd option for apps is to back them up with something like Titanium, and restoring them on the new device. There are apps out there that will also backup and restore app data. This is helpful if you want bring across your game progress, files, etc. BUT if the new phone is running a different OS version, you might be better off just installing everything from scratch and not migrating data.
Now, if you use a 3rd party app store, like Amazon's app store, you'll have to do those manually.
Next if you use the stock browser, you might have to worry about your book marks or favorites. I use Happydroid bookmark sort and backup (free in Play) to backup my bookmarks to SD, then bring them across (via dropbox, copying SD to pc, etc).
For SMS messages, I use SMS Backup + from Jan Berkel, it can upload your SMS & MMS messages to your google account, and restore them to your phone. It does call history too. It can't restore MMS messages to your phone though, but at least you can view them in gmail (it labels the messages as SMS).