>>>Should I take system image also ?
Personally, I'd say it is most preferrable. It can be used to rstore your system should it went belly-up.
>>> If yes - where in same external hard drive?
My external hard drive will automatically set up a folder at the very first time of System Image backup. Subsequent backup will be in that folder.
My external hardrive also names the folder as WindowsImageBackup under which is a folfer t-4-2-PC.
>>>Can i store both - system image and back up in one external hard drive??
Of course. They will be stored under different folders in the external drive.
>>>for example partition of my C drive and use windows 7 software for back up etc
If you meant .....partition C drive for system backup, my reply would be " no ".
Never backup anything into an internal partition, because if your hard drive fails, so go all your system backups.