Welcome to the Dragon Quest series!
DQ8 is a very comfortable entry point for newcomers, I think. It retains a lot of the series classic charm and difficulty, while still including modern amenities like a large, gorgeous overworld, solid development for the playable characters, and lots of strong voice acting.
The PS2 version of the game has nicer visuals and a fully orchestrated soundtrack that gives everything a majestic feel. The 3DS version doesn't look or sound as good, but it plays better, with two additional playable characters, some new postgame content, and little quality of life additions like being able to see the enemies on the map instead of random battles. It's a fantastic game, especially if you're like me and lost interest in Final Fantasy once every character started wearing a ton of zippers.
DQ3 is another excellent game, a very polished RPG for the NES era. This game introduces a class system to the series and lets you essentially create your own party (similar to the first Final Fantasy, but more balanced). You can also reclass characters past a certain point for unique combinations. The plot is tricky; some late-game elements feel much more rewarding and nostalgic if you've played the first two games, but you won't ever be lost or anything. I'd compare it to playing Wind Waker before playing Ocarina of Time; you'll still be aware of what's going on, but TWW's big mid-game twist would have a lot less impact without playing earlier Zeldas first.
I've only played the GBC port of DQ3 (released over here as "Dragon Warrior III") since the NES one is still pushing 60 bucks or so online, but the GBC version is great. From what I know, they've streamlined certain elements, introduced postgame content and a monster medal collecting system, added a major side quest (mini-medals), added enemy animations, and added a really fun and rewarding set of mini-games during the adventure. I haven't played the mobile version of this but I imagine it's similar. Just keep in mind that this game DID come out in 1990 or so, so you have to have a particular patience for these kinds of older games.
DQ5 (DS) is also a great choice because of its strong, poignant story, and it's also fairly brief for a DQ game at about 30-35 hours.
I haven't played DQ11 yet but people seem to love the PS4 version, and the upcoming Switch version is ridiculously upgraded in every way from before, with the exception of lower visual fidelity. We're talking tons more content, orchestrated music, a bunch of nostalgic postgame stuff, more ridable creatures, lots more side and backstory stuff on the cast, full voice acting, etc.
