Each app has sync (calendar, tasks). Contacts should be migrated to Gmail. The first time you do this is a bit of a schlep. But once it's done its gold.
First export to separate csv file all your contacts from your Android Phone, your old phone contacts, your SIM contacts. There are apps on android to do this (the default contact app should be fine). Take these csv files from wherever (PC, iTunes, Android SD card), and import them to your Gmail contacts on a PC web browser. Then do a merge all duplicates in Gmail. Manually check everything is ok, you don't want to be phoning the mistress instead of the misses. Also you might want to ensure your "My Contacts" only include your personal contacts and not randoms like firstname.lastname@example.org
Then on your Android disable phone contacts, kies sync, SIM contacts , i.e. hide them in the contacts app and disable contact sync in settings> accounts. In the same place make sure Google contacts is set to sync. Now you never have to worry about losing your contacts ever again. Once you're sure all your contacts are on Gmail, delete your phone contacts, kies, etc etc.
Calendar. What are you trying to sync? Google? No brainer. Exchange ? No brainer. If it's offline in Windows or something, then again move it to Google, or use Google calendar sync on your PC.