You are referring to selective backup.
A true back and recovery program like Acronis True Image or any other backup program used for commercial and home products, encourage full backup routines.
You start with a full backup. Which is an image that can be restored.
And either you do full backups on a regular schedule, or incremental or differentials on a regular schedule.
Yes, you need a second partition (not recommended, because if the drive dies, so go the backups)
Or a second Hard Drive (internal or external), network location or Optical.
However,, you can set it up to only back up certain folders and files. But that is not a true backup routine. That is a selective backup routine that is not commonly used outside of Windows Backup. It's not the norm and it's not encouraged. Though the option exists.
I encourage you to do a bit more research on the subject.
I would also add that most (Acronis especially) have the option to mount the backup as a drive and recover individual files. Acronis, I believe, includes an option to mount the backup and add/replace files in the backup itself.
then when I tried it it was going to take several hours
Then you are doing something wrong, have a ton of data or something is corrupted.
For me, having a huge compressed file to restore is more hastle than just reinstalling Windows.
Again, you are doing something wrong, cause I can restore a backup in less than 10 to 15 min and be back doing what I was doing.