My old iMac crashed, what is the best way to access and transfer files and photos?

The best way to transfer your files would be to use your Time Machine backup drive with Migration Assistant on another Mac.

If you have no TM backup and the iMac cannot be booted normally or in Recovery mode, then about the only thing you can do is remove the internal drive, place it into an external enclosure and connect it to another Mac from which you can access the files stored on it. This assumes the drive is healthy enough to access.

You can try putting the broken Mac into Target Disk Mode so you can connect it to another Mac. The broken Mac will appear as an externally connected drive.

Transfer files between two Mac computers using target disk mode - Apple Support