If they are ordinary single-layer DVDs, aka DVD-5, then 1 DVD has a capacity of 4.7GB. 250 DVDs are 4.7GB x 250 = 1175GB which is equivalent to 1.147TB. Since a 1TB external HDD has an actual capacity of approx 931GB, it will fall short, so I recommend no less than a 2TB external drive. This, of course, assumes that the DVDs are full to capacity, which may not be the case for all discs, but it's best to work with the higher limit. It won't hurt to go above 2TB either.
What is on these 250 DVD"s is it backups from a Backup program?
If you are doing Full Backups using a Backup program from the same computer on to all these discs then There are a lot of discs that have the same information on them. The Windows OS won't change much, just your personal files. So, you probably don't need to backup all of your DVD's
Good idea to have them on a HDD, but don't throw away the DVD's. If they are precious you want to have at least 2 if not more copies of your pictures. You can also store them on a Cloud service on top of what else you are doing.
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