Dogi appears in every Ys game but V and of course the prequel Ys Origin. Not that he does much in I and II aside from get introduced and bust down a few walls. From III on he starts playing a bigger role in the story. Wait for XSEED to release Oath in Felghana later this year and you'll see Dogi's hometown. Geis first appeared in Ys VI (released as Ys: The Ark of Napishtim overseas, dropping the number) so if you want to see more of him, check that out. Go for the PS2 version, not the PSP one.
Oath in Felghana and Origin are a lot alike, but I think I have to give it to Origin in terms of gameplay, even if Oath's soundtrack is so good that it could, in theory, make it better than all other games ever made regardless of any other variables.
I also really liked Ys II (Complete version) and need to go through it again. Which means I might as well tack on a replay of Ys I, since it's so short and they're pretty much one continuous game.
Napishtim was decent. Not quite as polished as the games that came after, but a good first step towards renewing the series.
The gameplay of Wanderers from Ys, with all its wonky hit-detection and weird movement physics, makes me want to beat my head against the wall, and yet it nevertheless has it's odd charm.
I really need to play Ys IV. And I guess Ys V out of a sense of obligation, since I never hear anything good about it.