Where did you buy Windows 7? If you found "a real cheap version" on eBay it may be a repackaged Technet key: Blocked Keys (Was EBAY Keys)
I know of no Windows 7 for sale that doesn't offer the option to get a disk and you should have the disk - for reinstalls, repairs and to get the full value of your investment in Windows 7 which you own for life.
You can borrow and copy or find any Windows 7 version retail installer to unlock all versions and burn to DVD: Windows 7 Universal Installation Disc - Create
To upgrade within Windows 7 MS wants us to use Anytime Upgrade, however valid retail Upgrade keys will work if inserted in Anytime Upgrade during the process where it unlocks the few extra features in Pro. You don't have to do a clean reinstall in that case.
I back up Home Premium computers over the network by copying their active User files and image stored on a Primary partition to a backup folder in the C drive of another home computer running any version.
You might be able to avoid upgrading by instead using free Paragon 10 Backup and Recovery program which will automate image and file backups over the network, and make you a boot disk if you ever need to reimage unbootable Windows 7: http://www.paragon-software.com/home.../download.html
You can also invest in an external HD to back up all of your computers, even on a schedule.