I've always looked at the series like this:
Dead Rising: Best story, best characters, great layout, goofy as fuck (so much ham), thrilling story, acceptable combat and a lot of things to explore. Pacing is very good and when you're fully upgraded, the timer is an excellent challenge.
Contrast is used brilliantly, there's great build up then the way things get more crowded as the game progresses, all within a pristine shiny mall creates brilliant atmosphere, the best in the entire series.
Downside is the shit tier AI that frustrates more than it helps, a fairly broken weapon system (toy chainsaw + 3 books = ultimate destruction) that either makes the game a loving good time or a broken piece of crap and vehicles handle like ass. It is also a 10 year old game and it feels like it at times, a bit janky, jittery and doesn't have the best flow.
Dead Rising 2 Good story, Chuck rules, good characters, an ok level layout and the weapon crafting is amazing. Still goofy but strewn in with some great drama, although the thrill is somewhat gone. Combat feels a bit better, however the formula feels a bit worn out.
Downside is Zombrex mechanic has more crushing weight than the timer in the first game, watching that clock tick down to your daughter dying is pretty distressing and if it was their desire then they nailed it. But on initial playthroughs it was tough. Combat is still janky and for an action game that feels like a new age beat em up it was pretty weak at times. The levels get dull fairly quickly and exploration isn't as exciting. It's also painfully slow to get started, Chuck moves like a complete tool and takes far too long for things to get interesting. The whole package is okay, but it feels generic to a degree.
It was still a good game.
Dead Rising 3
Characters are ok if uninteresting, combat is fantastic and the weapon combos are brilliant. The method to keep plans, find stuff early, do whatever just feels good.
Downside is the level layout and fetch quest style gameplay. It doesn't quite have that open world feeling, but it plays shitty like most open worlds do. Go here, do thing, go here, get reward. It gets boring very quickly and is ultimately forgettable.
The level design is shit tier and it looks fucking awful. Way too dark and gritty with too much emphasis on bleak atmosphere. The lack of contrast is annoying.
I'm keen as all fuck for Dead Rising 4, but they need to look at what made the first one so memorable in light of it being a launch window title. Ambition drove that game to be the quality it is now, formula could drive 4 to being a forgettable adventure that 3 was.
If I only pickup one of these just now, DR1 or DR2?
It seems most praise DR1 more.
I think play them in order, DR1 is still quite good after the first hour or so, DR2 takes too long to get going and doesn't feel as good a product. It's also very impressive for a 2006 game and what Capcom had in mind for the time is seriously impressive. Although they felt short of having a goal where you could pick up any object in any store (processing for that alone doesn't exist yet) they still designed a great action game with a solid story. Plus Frank is a dumbass who is great.