Q: Backup solution for Mac Mini late 2009?

My tech support left me and took backup drives with him, so I'm seeking a new solution.

I have a late 2009 Mac Mini. My current network connectivity is spotty, and is not under my control (or could be Mini's antenna; no idea). Therefore, I'm seeking a plug-in solution. Right now I have about 200 GB on my computer, and don't expect that to grow significantly. Can someone recommend an economical but reliable backup drive ? I have Time Machine, though don't know how to use it yet.

If I'm going to spend over about $40, I'd hope to get something that is also compatible with current low-to-mid-range Mac Mini, as that will almost certainly be my next computer. Thank you in advance.