I had a bunch of nice, technical reasons for my conclusions (and for keeping old computers), but... really, not particularly relevant. You want to buy a Macbook.

I say buy a cheap, refurbished Macbook with full warranty (not just whatever warranty is left), store your Mini while you're gone, and spend whatever you save on a more reliable backup solution (SSDs aren't necessarily more reliable). Multiple, automatic, incremental backups are the way to go. Apple hardware may have the illusion of being higher quality, but all hard drives are made by the same few manufacturers, and laptop hard drives are notoriously unreliable. Assume your laptop's drive will catastrophically fail, and spend accordingly.

Between music, movies, and photos, I'll assume you have 50GB, maybe upwards of 100GB of data you'd prefer not to have lost. Not only would it take years to get it uploaded, but a decent buffer of having 200GB of space on an Amazon Cloud Drive costs about $200 a year. It's a nice service, and allows you to not have to worry if your laptop is destroyed, broken, or stolen, but it's impractical for people to store the entirety of they want to have reliably backed up.

Time Machine does a good job, but it doesn't work (or at least doesn't work well) over the Internet. There are other solutions, but they are slightly more technical... and might involve keeping computers / hard drives at Josh's house. Inquire further if you're interested.