I, too, have thousands of digital photos which I have backed up on two internal hard drives, two external hard drives and a dedicated NAS (network attached storage) with redundancy in case one of those mirrors goes down. Thus, I have a minimum of 6 on-site backups. I also have three off-site backups—two external hard drive at a two different family member’s houses and one with one of the many cloud services that are available these days. These three backups serve as peace of mind in case my house goes up in flames, God forbid. I used to do backups to DVDs, but at 4.7 GB or 8.5 GB each, these can add up in a hurry and aren’t really cost effective in terms on time required to create them (possibly with printed labels) when they are compared to 3 TB hard drives (equivalent of about 640 single layer DVDs) that are about $120 or less each. I don’t worry too much about prints because anything can be reprinted, but I do keep a catalogue of thumbnails organized by year and/or event to help facilitate locating images.
Maybe I’m being a little anal in my backup strategy, but I feel that having having too many backups is better than having too few because these files represent precious memories that can never be replaced. It’s quite easy to drag and drop folders from one location to another for on-site backups and you can do several at once if you can handle the computer being that much slower or you can go do something else while it does its thing. The off-site backups I make a point of doing quite regularly so the amount of files from one time to the next are not excessive and don’t take all day to copy over the Internet.
In short, you should back up all those digital photos that are important to you, which from your description sounds like just about everything. 🙂 I would start with at least two on-site backups, at least one of which should be an external hard drive that you can quickly grab if you can when you are faced with a disaster of any kind. Then I would consider an off-site backup, either through family or friends and even a service like Livedrive, Carbonite, Google Drive, or Microsoft Skydrive. Each have their own initial storage capacity and price structure for additional space.
Once you clean up your current computer, you can also use it as a backup source if it’s on your home network. That’s my 7th on-site backup which I forgot to mention above. 🙂 Having that extra computer with your photos means that other family members can access those photos and videos without being at your new computer or hogging its resources.
Your new computer should be fast enough to handle the largest of your photos or videos. Having a fast processor means nothing without sufficient system and video RAM to back it up. What you choose to spend in that regard depends on your preference for Macs or PCs, too. 🙂
Anyway, any or all of what I’ve said, you may already know. Good luck in your backup strategy and may you add many more digital files of memories for years to come.