Low performance machines with minimal hardware can do the job, but it would need a lot more processing time, emitting heat and noise even with minimal tasks, depending on the task and the size of your library. Even with a music player like MB, some tasks are CPU intensive, including volume analysis, format converting, editing tags and then rewriting multiple files, displaying wave bar for lengthy tracks, running milkdrop visualizer, caching album art and artist/movie backdrops for artwork view/compact player/theater mode. With the general technological advances, MB is evolving as well, for instance, supporting hyper-threading, multi-core uses, etc.
I would recommend at least 4 GB of memory and i3 or i5 Haswell level of cpu and graphics performance for a pleasant MB life (last year I made a transition from a Core 2 Duo to an i5 laptop, and that made a huge difference in every regard). USB 3.0 ports can shorten backup time to external HDDs, and installing OS and apps on SSD would boost performance significantly (but not for storing music files unless you can afford it).
For screen size and resolution, the bigger and higher, the better, since you could display more info/windows/apps on the screen. Note that if you're using higher than 100% of DPI setting, some part of MB panes might not be visible. With a machine with high-resolution on a small screen, your best option would be using bigger fonts with 100% DPI setting.