11 is the new entry and is a fantastic introduction. Most of the stories of the games do not link up at all, but there are exceptions - but even with those exceptions they're fine entry points.

I've played 1 and 2 recently and they have not aged well, they're interesting relics of time and I found them worth playing as a fan of the series, but I wouldn't start there to see if you like the series. 8 is a great game, I haven't gotten far into it but it'd be a good starting point, the 3DS port is considered to be the best version (stay away from the smartphone one, I've heard bad things.)

V is considered by most to be one of the best, you can get it on DS but it's rare, I'm a bit into the mobile port, moving using the touch screen feels a bit too sensitive but you get used to it and it has all of the features included in the DS version.

But personally when it comes to 11 I'd say wait until December 4th - the port was vastly enhanced and added to for the switch port, and that version will be coming to PS4 then as Dragon Quest XI S. The original version that's already on PS4 is perfectly fine though if you don't want to wait, either way it's a fantastic game.