Moving the images to the cloud is one option, but if you do it, be aware that moving images to the cloud means they become cloud copies that are completely and permanently disconnected from any folder organization at your Mac. If the folder organization isn’t important to you, you might find this acceptable. But if you need to continue to manage the photos locally, then you should pursue a non-cloud option.
If the images are moved to the cloud, you will primarily need to edit with Lightroom (cloud-based), not Lightroom Classic, so edits you make to cloud images in Lightroom will not affect the images still on your hard drives. Although you can edit cloud-based images with Lightroom Classic, only one catalog can sync to the cloud, so the catalog you use to edit them when away must be the same catalog you use to organize it at home. Also, Lightroom has fewer features.
If these complications are too confusing, then you will want to stick with the annual version of your current plan level, and use a non-cloud option using Lightroom Classic only. A popular way is to do what you said:
Can I just take the HD with me and then bring it back when i return home? will it sync?
By @jjod
Yes, just take the external volumes with you and plug it into the computer you will be using when away. (If the volumes are formatted using an Apple file system, then the other computer must be a Mac.) At the other Mac you will also need to download the Creative Cloud desktop app, so that you can install Lightroom Classic on it. Make sure that other Mac meets the system requirements for Lightroom Classic 14 if that’s the version you’re using on your iMac.
What will not be on the hard drives are your settings and preferences files, which are on your iMac, so you may want to research how to bring those with you too. For example, Lightroom Classic can be set to store presets with the catalog rather than in the usual central location on your iMac. But that still doesn’t cover the application preferences.
The main thing to keep in mind is that a Lightroom Classic catalog tracks its images using file paths, in exactly the same way that websites, video editing apps, and page layout apps track imported media using file paths. There is a chance that when you plug your drives into the other Mac and open the catalog, everything will link up properly because you haven’t changed any file, folder, or volume names so the paths should be the same. But in case the catalog indicates that images can’t be found, know how to show Lightroom Classic where the files are so that it can re-link to them.