I've never played the original, though I'm going to keep my eye out for it if I can find it for under the $40+ most Atlus titles tend to command. The game's a sequel in the gameplay sense but not so much in the way of storyline (not that there's much anyways), and I've never really felt like I'm missing something that was explained in the first one.
The first handful of battles are indeed a bit tough; basically you're thrown in one end of the first maze and told to make your way back to the entrance, while of course mapping out everything along the way. With limited chances to heal and whatnot, it's a bit tough, but after you start figuring out your plan of attack in battles (As in which monsters to concentrate on first, which of your party is most effective in finishing the monsters off in a hurry, etc.) it gets a bit simpler. The game is great for on-the-go, as you're never really stuck in any place you can't just save it and turn it off. Besides, after you've finished the first quest, you're pretty much on your own, and the gameplay progression goes something like: go into first level; kill monsters until party is low on health and healing items; return to town to sell loot, buy weapons, and rest at inn; rinse and repeat. It's nothing you'll be too sucked into that you won't want to bring it out on the bus for fear of being in the middle of something important when your stop comes. All in all, I really like it. The gameplay is very very oldschool and pretty challenging, but the graphics and music make it a pleasure to slog through the same dungeon numerous times.
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I also picked up Castle of Shikigami III the other day for the Wii. I remember giving it a go a few times in my local arcade in Japan, but always left it for the more familiar part II. Now that I'm not paying to give it a shot, it's really a lot of fun--solid, and the same balance of difficulty and grazing opportunities. Sadly (or gladly for some, maybe) the story translation and voice acting are actually reasonably decent this time around; I was always amused by the horror that was Castle Shikigami II's translation. It put it in the same "so bad it's kinda funny" league as Plan 9 from Outer Space, in my opinion.