You stated that the info you want stored is 'extremely important'. In that case, don't be fooled by the convenience promised by cloud solution providers, but make sure that they, your ISP, the infrastructure and yourself can deliver on that promise. If you have doubts, use a pen drive or portable hard disk for backups.
-Shades
(as long as you're comfortable using cloud) I'd recommend using both.
FWIW I use SpiderOak for online backup. I dont pay much attention to it (probably should check it and test it more..) so cant really say much about it.
and use Syncovery (software) for local backup -- it recognises moved files and adjusts accordingly as opposed to deleting and copying again which is great, esp. when backing up to flash drive. Also does partial file backup, great for backing up large files with small changes. There probably are cheaper options out there (but note: updates are often, but paid upgrades are few, so in the long run it's actually very reasonable software). Also note: Syncovery can be used for online backup -- I did use it for one job to amazon S3 (over a period of a couple of years), but havent used it that way since.
If you have an extra partition on the laptop, you could always do backups there and simply sync these to external-HD/pen-drive. It's important to keep at least one backup off-site (I'm not good at keeping this going myself..).
A problem I find with my backup is that it has grown organically. I recently made the mistake of moving one group of files to a new more logical location, but the new folder wasn't backed-up. Of course that was when I deleted half the content of a file and clicked save :-/ (luckily I still had a recent enough backup).
But point being, try keep a good overview. Really, file organisation, planning of hierarchy etc., should be done with backup in mind. (But that's easy to say in retrospect!)