All opinions will be welcome
A month ago I would have said jump straight to Voyager. Like Alexis, I'm a big fan of the show and Janeway, as well as the brilliant character by the name of Seven.
I watched and enjoyed DS9 in the 90s, but not in the same league as Voyager. It was much darker and sometimes it felt boring.
When Ensign Ro came into TNG I suddenly had this thirst to learn more about eh Bajorans and I knew that was a focus on DS9, then we started to meet Cardassians in TNG and my thirst grew stronger.
So with a new found curiosity in my I decided to watch DS9 again and so far I've been completely blown away by how addictive its become. The characters on DS9 feel much more real than those on the starship, there's so much more diversity on DS9 that it doesn't matter about flying around space discovering new worlds. There's much more depth and the ensemble cast of characters are what's making it feel still fresh some 20 years later. There's more continuity too which is a bonus for this type of story-telling.
In a way DS9 still has that 'uncharted' feel TNG has has because of a stable wormhole, but that will be explained more in the pilot.
I would definitely recommend doing DS9 next and then finish off with Voyager.
I've also been (secretly) hoping that Alexis might find his way back to DS9 and I honestly believe he will see it in a different light to what he saw when he first watched the show.