Doug, streaming is "just another content source" and no different than using recorded media like CD or others as well as the radio. The advantage over the latter is that assuming a reasonably good Internet connection, streaming tends to provide excellent sound quality. (HD FM radio is actually pretty good in that respect) Streaming also gives access to music sources that you can't pull in "over the air" locally. I'll refer to my back and forth with Glenn up above about WXPN.ORG in that respect.
You may be able to find a decent "shelf system" second hand that would meet the needs you state in your last paragraph. Check all the usual suspect sources for used stuff as well as local charity retail operations that take donations that include electronic gear. Once you have that in your shop, most of those systems have an AUX input so if you decide you'd like to try streaming and have Internet access available, you can get an inexpensive device to do that.
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The most expensive tool is the one you buy "cheaply" and often...