Couple of tangential thoughts:
Backups are better with several sets of media. What if you backup to the external drive and then when you need to restore from it there is a fault on it, or the area on it where the files you need reside?
Will it be off-site? i.e. survive a fire in the primary location. One answer is to have, say, two drives and take one with you to parents / in-laws each time you visit
them. If you are going to do that then a somewhat more rugged drive that will survive being carted back-and-forth might be worth looking for.
Also, best to have more than one copy of your files. You might modify a file, wrongly, today, then back it up, and THEN realise that the most recent change you made was duff and want an EARLIER version back again.
You can achieve that on an external drive by making folders at root level of 31Mar2015 etc. and then copying everything off your C: drive BELOW that point on the external. When it gets full delete the oldest root-folder to release the space. On that basis you might want a larger drive so it can hold several copies of your C: drive. I doubt that a Terrabyte (or even a multi-Terrabyte) drive is much more money than a 500GB one.
Yet another alternative is to use an online backup service. That will send just your changed files over the internet to the "cloud". That will store a number of previous-versions and so on and won't run out of space :) - although they'll charge you more if you use more ..