Both are great games (with expansions, the base games shouldn't be considered) so both are excellent choices. Since you never played the series I suggest Civ V: Civ VI can be quite overwhelming for a new player and it needs time to learn it, while V is a little simpler and straightforward. Also Civ V is cheaper, so if you don't like the series it's not a problem and you can always get VI in the future since they are quite different experiences.
Not only new civilizations and game modes, but the expansions adds several new systems, victory types, resources, gameplay mechanics ecc. ecc. The game before and after the big expansions is completely different.
Barbarians at first can be quite a problem, expecially in Civ VI. Try taking them slowly with hit-and-run tactics until your units get some experience and don't send your first warriors too far too quickly, expecially if they are alone. Make a priority to explore (not necessarily killing everything on sight!) your surroundings, searching for camps to avoid having too many barbarians around you.
Also, if you want, you can remove them from your game. When you start a game you can change a lot of the rules to better adjust to the experience you want.