With Lightroom CC you can simply back all your photos up to the Cloud and can access them from another computer so they wouldn’t need transferring to that computer.
Cloud storage comes at a cost though, so do you intend to keep them in the Cloud permanently?
Also, and probably most importantly, do you currently use traditional folder based Lightroom (6/Classic etc.) and if so, do you intend to keep using it? As using Classic and the cloud based CC together has many caveats.
I'm not sure how long I plan on using the cloud but have no plans to stop using it in the foreseeable future. If I do decide to stop using, could I transfer all the photos off of the cloud and onto a new computer?
I am still using the traditional folder based Lightroom. Is there a better way to organize photos now? I have had Lightroom for about 6 years and haven't updated my organization method to keep up with the updates but am interested in doing this if there is a better strategy and it's not too complicated.
I use the Adobe Bridge | Camera Raw | Photoshop workflow.
The best place to fine info on that is YouTube - Julieanne Kost and/or Terry White have how-to videos there.
As far as cloud storage, I guess I'm lucky.
I have a hosting account (Godaddy) so when I want to store files I just FTP them to a folder on their servers.
It may be a lot faster and easier to use an external USB hard drive to move image files to a new computer.
Have you considered that as a method?
I think it all depends on your workflow, what kind of edits (if any) do you want to do on the second computer and if you want the cost of Cloud Storage...... or even need it.
It's worth watching these videos to see if you want to go down the CC route:
And reading these threads: