I use Mozy for my backups. I have not personally used Carbonite, but I have heard from multiple people first-hand within the past couple months who have dumped Carbonite in favor of Mozy and have gotten better performance. Carbonite offers a trial, Mozy offers 2gb totally free. I personally would recommend setting up a free 2tb version just to get a feel of it. I use that on my wife's laptop; it's plenty big enough to back that up. My own backup is right about 1tb now; it will be more than that when it finishes backing up the photos from my latest trip!
I am a big fan of online backups because hard drives are so unreliable, and they can often develop bad sectors which you would never notice unless you tried to pull data off them. In other words, you may connect your external drive and it looks fine and you can copy data to it, but meanwhile some of your existing data is gone. The only way to know for sure is to do a full sector scan on it, which is time-consuming, especially on an external drive. Plus, with external drives, you need some form of backup software or at least a folder sync program. Free/cheap backup software often tends to be a little bit flaky so you need to keep an eye on it.
That being said, Mozy/Carbonite are not places to keep photos to work on them - they are strictly for backup. The originals you can keep on an internal or external drive. There's little reason not to store them on your internal drive, unless you're running out of space or you want portability. (This is a good time to put in a plug for shooting in Raw mode - even if you don't want to process the photos now, you may want that ability later and shooting Raw now lets you go back in the future to edit today's photos.)
For editing software, definitely try a trial of Lightroom, and it may not hurt to check for some basic training videos (there are probably some on YouTube and on Adobe's site)... it's extremely good as managing your photos as well as "processing" them. By procesing, I mean cropping, rotating, adjusting colors, brightless, that kind of thing - you'll need Photoshop to cut someone's head off and put it on another body, but Photoshop can't manage your photos like Lightroom can.