You should be "OK" with a mid-2010, but it REALLY depends. If you're transcoding any material to iPads etc - especially modern stuff - it might be a tad slower.
But it depends on what you're playing. What's your usage style?
We mainly stream films via Plex through ethernet cables and 500MB homeplugs to an AppleTV or PS3, no wireless involved.
I MAY try accessing films remotely from my iPad when travelling, also.
Otherwise, just being able to have Time Machine backups of my iPad and also my Macbook, when travelling.
I may also move my iTunes library off my iMac onto a hard drive connected to the Mac Mini, so that I can play music through my Apple TV, without having to turn on my iMac first.
How does all of that sound?
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Actually, my iMac is mid-2010! How time flies.
I got it in early 2011.. Although it's quad-core i7 with 12GB of RAM - which seems more current than a five-year old computer usually is?
Hard disc is painfully slow though.. SSD conversion is overdue!