Well, IF you need to Partition and Format, Win 7 makes it relatively easy. You use Disk Management to "see" the HDD you want to work on. If it already has one or more Partitions on it that you do NOT want to keep anything from, you can RIGHT-click on each and choose to Delete it. After doing that I would back out and reboot to be sure Windows has the info correct in its Registry (may not be necessary), then go back into Disk Management. Now the HDD is exactly like a brand new empty HDD. You use Disk Management (again) and RIGHT-click on that HDD's Unallocated Space and choose the "Create a new Simple Volume". This will actually do both the Partitioning and Formatting in one combined operation. You will be offered a default group of settings which you ca approve or change. Usually there are only two things you MIGHT want to change. You may want to customize the size of the Partition you are creating. And the Partition does NOT need to be Bootable if you are going to use it solely for data, and not try to put an OS there to boot from.
HOWEVER, your case might be slightly different, depending on how you plan to do your backup system. If you plan to buy and use a backup software package (or download a free one), follow its instructions on how to set up the HDD that receives the backups. On the other hand, you started out proposing to use a cloning tool to make a complete clone of your C: drive to the second HDD. Now most clone tools I've used include menu choices to Delete any specified old Partition if you need to. And virtually all will do the two initial steps - Create a Partition and Format it - for you as their first steps. If you are cloning a bootable HDD, it will automatically make this clone Partition bootable, too. so if you are cloning you do NOT need to Partition and Format ahead of time.
The "original backup plan" you outline includes many parts of a standard plan. I think you would find it much easier to do that using a backup software package that can keep track of all the changed files that need inclusion in each day's incremental backup. It is almost impossible to do that manually and simply copy files every day. And a cloning tool will not do that.
Your plan does have flaws, though, compared to an optimal backup system. One a backup is made to some storage medium, two things should be done with it. It should be disconnected from all electrical power to prevent accidental damage. And it should be removed and stored in a different location. These two steps prevent the following kinds of damage to the backup:
1. Accidental alterations by writing to the wrong drive.
2. Alterations due to acquired malware on your computer.
3. Power surges and sags.
4. Flood, fire, theft, etc. at the computer site.
For all these reasons, mounting your "backup" drive inside your computer permanently is a bad idea. The most popular type of backup device for home users is a portable hard drive which you can plug in to make a backup or restore, and disconnect and remove to another location when not doing those operations.