The servers keep track of which cards you own, so it's really easy and you won't lose any of your cards when going to a new computer, you only need your account :)
But step by step, just to ensure it's clear:
1 - Install iStripper on new computer.
2 - Login to your account.
3 - Download your cards (though with your large collection, this might take quite a while).
4 - Enjoy!
If you do experience problems, in the settings menu at the top there is the button "Rebuild collection" which you could use in case your cards aren't being downloaded properly to the new computer, again this can take quite a while.
Side note: In case you are taking the hard drive containing you cards from your old computer to your new one, between step 2 and 3, in the settings menu under the header data, set the storage folder to where all your cards are saved and then hit the "Rebuild collection" button. This should save you a lot of download time.