I would suggest that you use a CDN to host your image files.
For starters you could move the images over to the new hosting though. Or is it many terrabytes of images? If so, I don’t think it’s a good idea to have them in WordPress.
Regarding hosting the image library, have you considered using a CDN?
There are a bunch of plugins that would help you with this, they are all pretty straight forward:
- https://wordpress.org/plugins/w3-total-cache/
- https://wordpress.org/plugins/amazon-s3-and-cloudfront/
- https://wordpress.org/plugins/aws-cdn-by-wpadmin/
- https://wordpress.org/plugins/cdn-enabler/
Personally, I’ve ended up using WP Rocket: https://wp-rocket.me/
It’s working really well, and there are a lot of settings to tweak performance.
I’m using S3 + Cloudfront from Amazon on some projects. My favourite one so far though, has been StackPath: https://www.stackpath.com/, it’s running really nice with WP Rocket.
But before you enable any CDN, I’d actually move over the images to the new VPS. I assume that you will be keeping the whole website, all posts etc.
- Dump the DB on the old site
- Copy the files from the old to the new using rsync, directly from the old server to the new.
- Import the DB dump on the new server.