WIFI sync iPad and iPhone with new computer?

Question

Bought my iPad in the fall, but didn't sync with my iMac because it was old and performing miserably, and because I was waiting for the MacMini to get a refresh so I could use it as a Media Center. Well, now I have my shiny new MacMini, but when I go to my iPad settings to do a wifi sync, it says it will sync next time I'm near my friend's computer. This is strange, because the only time I've EVER hooked up to a computer was once, at his house, to charge up and copy a book I wanted. I did not do anything except drag the book to my iPad in the Devices list on the left (older version of iTunes). I've read on other boards that I have to right click on my iPad and "transfer purchases" but when I connect my iPad to the MacMini by USB, all it gives me is the "Welcome to your new iPad" screen, with the option to set up as a new iPad or restore from a backup. Right clicking merely asks me to eject or restore. The only backup listed is dated April 21, 2011, which is an old iPad that was stolen. I've been backing up this current iPad with iCloud and have never had a problem, but it would be nice to sync over wifi if i want to copy files or music, instead of relying on Dropbox all the time.
Simillarly, when I try to sync my iPhone, I get as far as the syncing options, but when I go to apply the changes, it warns me that my phone is synced with another computer and that I can proceed if I want to erase this phone and sync the contents with my current library. In both situations, I'm afraid to proceed because I don't want to lose vital work information that has been stored in various apps. Any words of advice here? I know my apps are backed up, but I don't want to be surprised by finding out that the apps were backed up, but not the data I entered into them. I previously followed a tutorial which claimed I could copy and edit a file from the original iMac and transfer it to the MacMini, forcing it to recognize my new compurer as the original library... so when I open iTunes on the new computer, it does load up the iPhone and recognize it over wifi, and I can fiddle with options without having to connect via USB... but I get halted by that warning, and the settings app on the phone itself still indicates my original library as the one it needs for wifi sync. I should also add that my original iMac indicates that I need a newer version of iTunes to connect with my iPhone's iOS, but it is also too old (it's Lion) to upgrade iTunes beyond it's current version. I feel like with all this amazing technology, the options for a person who buys a new computer but doesn't want to migrate the clustered mess of their old system... still shamefully limited... unless I'm missing something.

Answer 1

Hmm. That sounds easy enough... but how do I backup to the new computer when it doesn't give me the option? When I connect the iPad via USB, it asks me to:
• set up as a new IPad
• restore from a previous backup (where the only backup listed in the drop down menu is a stolen iPad with outdated information, dated April of 2011. It doesn't ask to restore from iCloud where this current iPad is backed up.)
If you're suggesting that I back up both devices to iCloud and then wipe them, then plug them into the new computer and restore from the iCloud backup, so that my new computer considers these new devices, that makes sense... except that I don't see an option to restore from iCloud. Does that option appear later? And is it absolutely certain that any app I have entered data into will restore that information as well, and not just the app? For example, if I have an index card app which I make essay notes in, will those notes definitely be backed up along with the app? Or just the app? I can't afford to lose all my work data.
Thanks.