Mac Mini SW upgrade

No. Back up your data,check your applications for compatibility, buy Snow Leopard, update to 10.6.8, click here, and download El Capitan from the Mac App Store without installing any other intermediate versions.

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It's in the online Apple Store, not the Mac App Store. Click here.

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Mac mini, Mac OS X (10.5.8), Intel Mac Mini 2,1

If your notes are correct, and you have a Mac mini 2,1, then Lion (10.7.5) is the maximum OS X version for your model. It's not available on DVD, but can be bought from the App Store app.

Note: You would need to buy Snow Leopard on a DVD, install it, and update it to 10.6.8 to get the App Store app.

Yep, Niel is correct.

Just to note, make a full backup of your system before upgrading, preferably a clone. If I had only the choice of either running Snow Leopard or Lion, personally I'd stick with Snow Leopard.