I've had issues in the past when I used one backup provider/software program for both online and local backups. If something went wrong with one (it stopped backing up unexpectedly without notifying me, an unusual character made a particular folder or file not back up, etc.), it went wrong with both and I was out of luck. So even though I could use Crashplan for both, I don't. I use Crashplan for online backup. (I recently switched to the Small Business plan--home users can use it, too. You might need to double check what I said about EHDs with them. The home version did both, but I didn't pay attention to whether the business version does.) My EHD is a Passport Drive from Western Digital, and I just use the backup software that it came with for local backups.
There is a built in backup with Windows, but I didn't like it when I tried it. I tried a few around the same time, so it's possible I'm mixing it up with another program, but I think the problem may have been that it was too simplified. I didn't have enough control over exactly what was and wasn't backed up, and I couldn't see how much was left to do while it was working.