If you are a scared baby and cannot handle some gray market hi-jinx, I will direct you towards your local where you can purchase a variety of Classic or Mini consoles and game compilations. No, downloading other people’s copies of games you don't own is definitely not legal. Yes, 'backing up' games is entirely legal and downloading other people's backups of games you already own might be legal (but nobody has tested it in court).
Yes, emulation software is entirely legal. I will begin this guide by asking you to check your internet law degree at the door.