700 GB is almost certainly enough for the photos, unless you take an extraordinary number of pictures. For example, my desktop backgrounds folder, where I grab nice pictures from the net has over 7,600 images, but only takes up a little over 7 GB. 1% of the space on your drive.
OTOH, I also record amateur sports videos. My hockey games are a little over an hour long, and each one adds about 8 GB/hour of video. So, 700 GB would hold less than 100 hours of video. 100 hours is a lot, if most of your videos are 30 second clips of your pets, or a minute of a fireworks show, etc. That would be 6000 one minute videos. Again, for most people, plenty of space.
Can your older machines connect to your network? If so, then you can share a folder on your HP and log into it from all of the other machines. You can search for how to do that. I found one at Tom's Hardware. (I'm assuming all of the machines are Windows. If you have some running other OS' then it'll take a little more work to share files between them.)
Transfer times will depend on the number and size of the files. Again, videos are likely to take more time. For most casual users, where it's probably just a few GB on each machine, it should only take a few minutes per machine. If you can connect one or both machines to your router with ethernet cables, then the transfers will be faster. But, both on Wi-Fi will work.
If some of the older machines can't connect to the Wi-Fi, then you can do what's called Sneakernet. Copy the pictures onto an external drive and carry them over to the other computer. You can use a hard drive, like Kees_B suggests. Or, you can get SD cards really cheap that will probably hold an old computer's entire collection. As long as all of these machines have USB. Which all laptops in the last 15 years do have.
One issue will be finding the images on the old machines. Did you have any organization plan on any of the computers? Did you dump them all under the "Pictures" and "Videos" folders? If so, then they should be easy to gather. If you kept some under your Documents folder, that's still fairly consolidated and easy to find.
If they're scattered all over your hard drive, then it'll take a little more work. For pictures, the vast majority of cameras save as .JPG files. So, you can go into Windows Explorer, double-click your drive. Then, in the upper-right is a Search box. Type in *.jpg and it'll find every image on your hard drive. A lot of them will be used by programs, and will not be anything you care about saving. So, change the view to "Details" and sort by "Folder path," and that way you can quickly scroll past large swaths that you don't care about.
Videos can be under a few different extensions. The most common are .mp4, .avi, .mov. How-To Geek has a description shows how to search for multiple extensions. Note that the "OR" has to be all caps. Ext:.mp4 OR Ext:.avi OR Ext:.mov
I agree with Kees_B, that if these pictures are important to you, then you're going to want to back them up. A couple of backup drives, whether hard drives or SD cards, is one way to do it. But, I find that I put off manual backups, and pretty soon it's been a year since I last backed up. So, I've set up automated systems to back up to a NAS locally and to a cloud backup for off-site. If your data isn't in at least three places then it's not really backed up. One thing I find that makes a NAS more convenient than a USB external backup drive is that I don't have to plug it directly into my computers. It sits out of the way, in the corner by my router, and all my computers can back up to it at any time. For me, knowing that everything is always backed up was worth the money.
I want to systematically go thru several lap tops, phones, and clouds. extracting every personal photo and video from each and transfer them to a dedicated HP laptop. I am not concerned with organization at this point. just getting them all in one spot including those on google drive ect, even if i can only save copies.
I need a practical step by step approach. is 700 gigs on my laptop enough.? do i link lap tops via usb? do I use cdroms as i go? any help would be appreciated..... also getting my photos from facebook would be nice. thank you

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