There are several layers of compatibility.
My biggest concern is those DVDs. While some are simply discs filled with files, others use a proprietary system that might require running an app - if there's not a viewer app for Mac, life may get challenging.
The photos themselves are unlikely to be in a proprietary format. Mac can read a wide variety of image file types, so no worries there.
The formatting of the external hard drive is a compatibility factor - two factors:
Connection type - USB-A, USB-C, Thunderbolt. Obviously, that needs to be consistent with the connections available on your Mac.
Formatting - All external drives come pre-formatted from the factory, but you can erase and reformat any external drive to suit your needs, using Disk Utility on the Mac, prior to putting the drive into active service.
When a drive is advertised to be compatible with both Windows and Mac, it generally means it's formatted in ExFAT - a Windows format that Macs can both read and write (and you will need to be able to both read and write to that drive). If you want/need to connect the same external drive to both Windows and Mac machines, then ExFAT is the way to go. You can also use the MS-DOS FAT format for drives that are 32 GB or smaller (USB thumb drives).
If the drive happens to be formatted NTFS (Windows NT File System) then it will have to be erased/reformatted prior to use - Mac does not (natively) work with NTFS-formatted disks.
Some drives come specifically Mac-formatted. If you'll only be operating in a Mac world, it's a nice little convenience, but you may pay more for a Mac-specific drive than the convenience is worth.
I could go on and on regarding disk formats, but this should give you the basic overview.