Actually, you have a DQ remake for Iphone/Android, GBC and SNES all of them have attack animations but lack monster animations. Recommended since it’s a short game.
You have a DQ 2 remake for all of the above platforms above, again only attack for all of them, the magics are just a flashing effect btw. Not so recommended.
You have a DQ 3 also for all the plats above, “full” animations in all of them; the monsters are animated only during attack though. The three first games are a trilogy, The Iphone/Android remakes are recommended, the GBC not so much, the snes ones were released only on Japan, but you can find some unofficial translations around.
DQ IV, remakes for android/ios, DS and PSX (Japanese only) full animations. Highly recommended.
DQ V, remakes for android/ios, DS and PS2 (Japanese only) full animations, also highly recommended.
DQ VI, android/IOS and DS, full animations (even in the snes original, Japanese only) recommended, those three form sort of a trilogy also.
DQ VII and VIII, the upcoming DS remake/port, DQ VIII had a port for android/ios.
DQ IX DS only.
I also had the same reservations for DQ that you have now, but I gave the IV ds remake a chance and I can say that, in a story and narrative department DQ is miles ahead of FF, and since then I started to enjoy both. If you like a good story and can play DS, or Iphone/Android games give IV a chance, I believe you won’t be desapointed.