With a full OS image backup, you don't really need to keep a separate backup of your files.
But even if you wanted to do that, you can. When a backup of something is made it's like a zip file... they won't get mixed together.
Both backup softwares that I mentioned above, also allow you to make bootable rescue media. This will allow you to access your backups... even if Windows won't boot.
As for your 2TB external drive... you can make some partitions on it, if that's easier for you.
Like... maybe a 500GB partition for full OS image backups. And a second partition for storing files that you want to access on other computers as well.
A full OS image backup will be about 1/2 the size of the data on the C:\ drive.
If your 250GB laptop drive has... 100GB on it... the backup will be about 52GB.
For example, one of my drives is partitioned like this....
All this stuff can be accessed by whatever computer I hook the drive to.