In general, cloud storage is only a good idea if you don't mind the idea of losing all your work. Unless you have a provider with an SLA that guarantees availability, any number of things could take out your provider and leave you high and dry. For archival purposes, the easiest and cheapest approach is always going to be local storage. Cloud backups work well for off-site storage as a secondary backup (in case of local destruction) but they should never be trusted as your sole or primary means of backup.
As for the speed of uploading. Most residential connections have horribly slow upload speeds. There is no way around this. Any decent file storage site is going to take files as fast as your home Internet can provide them. There is no magical secret to making it go faster other than to buy a better Internet connection. If you want to verify if your home connection is the issue, I'd recommend trying something like Speedtest.net and checking if your upload rate differs significantly from your upstream bandwidth as reported by Speedtest.
Beyond that, there is nothing magical about cloud storage. You manage it just like you would manage a local external hard drive. The only difference is that you have no direct control over the cloud storage and it may have an option to be able to share your files out to other people. Some services are more targeted at images, offering features like the ability to resize, edit or sell the photos online and providing galleries, however that won't help you any with the pain and slowness of uploading a large number of large files.