A few days ago, someone gave me his old Roku Player. It's not the newest technology anymore, but since we have a wizard of repurposing technology around here, I was wondering if there's anything cool I could do with it.

Fraid I had to do some research on that exact unit.
Before I get too far, Roku has dropped support for the classic boxes. I hope that this doesn't mean that it is unusable. If true, you might be able to sell it, and get back enough to get a Roku 1. They're cheap.
I have a Roku 3 in our main room, a Roku stick in the game room and my sister's room, and a Roku 1 in my room and my parents room.
A basic rule of thumb, is the higher the number, then the better the specs of the unit.
Older units show some control delay, but so far hasn't been enough to make it unusable. while newer units are HDMI only.
I would connect yours to a CRT-TV, and connect directly to your Ethernet router.
All units I've seen are wireless, but I don't know if this is true for yours.

That out of the way: These things are rather fun to mess around with, just going through the channel store, or even finding unlisted channels.

First off, you will want to format it, and register yourself a new account at Roku's website, it's free.
Once that is done, you should be good to go with everything else.

If you watch videos on Youtube, Hulu, Vudu, or Netflix, these things are great for watching those your main TV.
You will need a computer to sync your accounts (In the case of youtube, to knock out the parental filter) but that is as simple as following a URL, and entering a short code. Afterward, the computer us no longer needed.

I've so far found that these units handle video streaming better than any computer I've used. This alone is well worth it.

My best advice to you, would be to poke around with it a bit, and see what happens.
You can't break it with the controls alone.