I have a Mid 2011 MBA w/ only 2 GB of RAM and the 1.6 GHz Intel Core i5. It's currently running osx 10.11.5. So far, I've not had any issues doing the basic tasks you listed, but then, I don't play CDs or DVDs with it because I don't have an external contraption for playing them, and in any case, all my owned music is loaded on my 2016 Mac Mini. I also don't game at all (no interest). I've never plugged it into my Mini's monitor either, though I could if I wanted to, but have no reason to.
I read online recently that Apple is giving all, or maybe it was only some, of their laptops some nice upgrades. Not sure when they go on sale though. You might want to look into those upgrades before purchasing a lower end, used Air, especially if you want it to last 4-5 years. I gotta say, I've been quite happy with my Air doing all I need with it, but I believe gaming requires more processing power than I have.
The MB I bought for my daughter when she graduated high school in 2008, before going to college, had to be replaced this year as it wasn't able to do much of anything anymore, outside of emails and document related things, even though she had upgraded the RAM in it to 4 GBs 4 years ago. It was too old to upgrade beyond osx 10.6.8. Streaming videos not working so well anymore was her biggest complaint. She's not a gamer either though. I also had to replace my old 2008 Mini this year for similar reasons.
If the used Air doesn't suit your needs in a few years, you could always sell it and get another used one with a newer processor and more RAM.