Based on what you have written, and therefore my assumptions about your technical capability, I advise that you get help from a person who is PC literate and can help you set up a new system and transfer JRiver and all your music/media files across.
If you are buying a prebuilt PC system from a business that builds PCs in house, rather than just sells boxed PCs sourced from elsewhere, then they would probably be able to transfer JRiver for you and get it all working.
JRiver MC is hard disk based. It doesn't have Cloud features, although it does have similar features. But they won't do what you seem to want, which I understand is when you install a new system, then log into your cloud service, all your music is automatically downloaded again for you. Again, I could sort of make that happen just for the music and JRiver library and settings, but not for the JRiver application, and it wouldn't be done by the JRiver application after you installed it either. It would have to be done separately. It wouldn't be automatic. It would have to be done by someone who knew what they were doing. If your music collection is large, using the Cloud to transfer it probably isn't the best solution.
So, my advice is to find someone local to buy the PC from and set it and JRiver MC up for you. If you have a friend who is PC literate and willing to help, that would be an option as well.