Do your backup overnight,i use Norton Ghost to do mine,However i do have USB 2.0.As for the extra card i use and recomend Belkin,works perfect for me,i`m running vista 64bit.All my 12 Usb ports on my pc work fine as well.
Have you upgraded to a 300GB HDD? I only ask as if your PC came with a 300GB HDD it seems inconceivable that it doesn't have USB 2.0 (i.e. USB 2.0 has been around quite a long time and it is unlikely that a new PC supplied with a 300GB drive would not have USB 2.0).
In any event, have you considered installing another hard drive inside the system unit for backup purposes (assuming there is space etc.)? The drawback with this is that, as such a drive is powered on all the time, it could be affected by other issues that might affect the PC at any time (e.g. malware, power surges etc.).
If you do want to consider an additional internal HDD and your system is genuinely USB 1.1, the HDD would surely be IDE / PATA type (i.e. not SATA).