How much you wanna store?
Most of the big guys give you 3-5 GB simply by signing up.
If it's hundreds of gigs, I'd take a look at an annual Office 365 Home subscription. Apart from Office for 5 computers and devices, you get one terabyte of cloud storage, plus an hour per month of Skype-to-landline/mobile calls, for around a grand a year. It's one of the great bargains in computing, imv.
OneDrive has been improving steadily. It's now perfectly serviceable, and it has decent mobile clients on all major platforms. And it's secure.