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The good thing about Linux is, it’s not very ressouce demanding. If you pick the xfce version of Mint, you can get away with 4GB of RAM. But you won’t have that much fun coding as soon as you start something more ressource heavy (big data sets, ML, …) so this depends a little in which direction you want to go. However see if you can find something used, preferably something you can open from the back side to upgrade components like SSD and RAM (cheaper than buying higher specs)
No, bluray is 1080p (or 2160p if UHD Bluray) while DVDs are 576p-720p (what looks really shitty on a 4K TV). I only buy BDs and UHD BDs these days