My PC is having problems and may have to be replaced soon. I looked on the iTunes Match support page and couldn’t find an answer to this question. If/when I replace this computer, will I be able to then download the stored music to iTunes on the new computer? Do I really need to pay $24.95 a year for Match, or is there some other music cloud storage that does the same thing, and that will talk to iTunes? I don’t need to have the music available across multiple devices.
Yes, you can download your music from iTunes Match to your new computer once it has been authorized.
Since you mention PC problems and lack of need to make the music available across multiple devices, it seems like your main concern is just backing up your music? If so, you might be better served just getting a small, cheap external hard drive.