Some things to ponder over.
1) How much space is used on the old Mac and what size is the new Mac's drive?
It is best to allow plenty of room on the new Mac for migration and growth.
Clean out the old Mac until there is 100GB less than the new Mac's drive.
Consider returning the new Mac and ordering one with a larger drive.
Free up storage space on your Mac - Apple Support
2) Yes you can move your photo and/or music library to an external hard drive.
However you need to use 2 reliable external hard drives for that.
One drive for the libraries and a one to backup the first.
Move your Photos library to save space on your Mac - Apple Support
Change where your music files are stored on Mac - Apple Support
3) How were you planing on Migrating from the old to the new Mac?
Large Network migrations are not reliable and prone to fail.
Ethernet to Ethernet is more reliable but very slow.
Using your Time Machine backup is best.
Transfer to a new Mac with Migration Assistant - Apple Support
Back up your Mac with Time Machine - Apple Support