Well a NAS Server has just as much of a chance as failing as a USB drive. Its not really the USB enclosure that dies but the Hard drive and ANY hard drive can Fail out of the blue.
Now I understand where you are coming from. I have 4 TB of data. Movies, Music, Games, All the scanned family photos and what not, phone backups ect all on that. What I do is I have another 4TB drive that I clone to and keep that in my safe. This way the Backup drive has VERY little use so it won't fail as soon and also my safe is fire/water proof as well.
Now a Cloud solution is a pretty good idea just because you don't ever have to worry about backing up anything. Its all done automatically. Now yes with your connection it would probably take a few weeks of just having your PC on 24/7 to do the inital backup but once everything is backed up its just the matter of what is new. and for 60 bucks a year for carbonite i think its pretty well worth it for people who don't want to deal with it. This is also better than a USB or NAS in a way of 1) a NAS server will be a few hundred dollars. 2) If your house ever blows up or catchs on fire or something and your NAS or USB drive is in the house as well (Knock on wood) Then buying all of that wouldn't have mattered anyways! Everything would still be gone.
In your case i would go with
In that order. A NAS is more for someone like me who has terabytes of data and whats to share it with everyone or have a constant backup.
If you know of anyone with a faster internet connection maybe take the PC over to their house for a few days if you get online backup XD speed it up a bit, But still the rule of thumb is have you data in 3 Places. If you want to be that prepared then do the Cloud and then a USB/NAS storage as well.