[twistedcheeslet]

Yes absolutely a Pi is likely plenty assuming it's fairly light load. That said, if you prefer x86 you may have better mileage using an older thinclient or perhaps even something like the ODroid H3 (or frankly any old laptop).

Just be sure to have a decent backup system in place as consumer grade equipment like the above may fail rather abruptly with little route to recovery.

Edit: you may want to check out Jupiter Broadcasting's Self-Hosted podcast. The show is very much geared towards DIY enthusiasts/small businesses.