Copy all the picture files, or do a search, and search only by file type(Picture formats) Jpg and so forth.
once copied, place them on an external USB and move them over, this will limit the speed to what the USB is capable of.
For the fastest results and easiest.
First make sure both computers are hard wired to the internet, Wireless is fine, but slightly slower.
Now open your laptop, right click on the folder or drive containing all of your photos you want.
Go to properties on files/folders/drive, now go to sharing, Click share this folder and create a share.
Now on the computer your moving them to, open up the computer screen, go to the left where you can see the directory, drives, and files/folders, Now click network, You should be able to see the target computer with the pictures, Now access that computer, you should see the drive containing all the photos there. Copy and paste them onto your target computer.
This should be extremely fast, it will migrate the files as fast as your harddrive can possibly handle, The fastest possible outcome.