Perfect games for the Nintendo Fan...hmmm? Ratchet and Clank is the PS3's Mario with guns. Little Big Planet is our version of Super Mario Wii except you get to create your own levels and sack boy. You did say no racers but Modnation is Mario Kart with customization and creation. Heavy Rain is a new experience you should try. Uncharted and God of War are givens. Demon Souls is hardcore crack.

Add in a little Pixel Junk Love, with a side of Flower, a dash of Shatter and some Super Stardust for desert and your good to go.

Definitely LittleBigPlanet.. umm.. other than that I can't really think of anything that hasn't been said... as for PSN games, Super Stardust HD is a good arcade pickup and play shooter.. all the Pixeljunk games (except pixeljunk racers) are really good. flower is good, echochrome is good if you like that kind of thing... also, its not PSN but you might like modnation racers if you're a fan of mariokart... 

Also I know you said you didn't want an FPS but I still highly recommend MAG because it is unlike any other FPS out there that I know of in that its huge games (64-256 players in a match) force you to play as a team if you want to have a prayer of winning and thus makes it a much more enjoyable experience then say COD imho. It is online only just fyi though...

My top five:

1. LittleBigPlanet
2. Demon's Souls
3. Uncharted 2: Among Thieves
4. Metal Gear Solid 4: Guns of the Patriots
5. Killzone 2 (yeah yeah, no shooters, but its still one of the very best on ps3)

And to complete the set (can't play one without the other!):

6. Uncharted: Drake's Fortune

LittleBigPlanet is easily the best game on ps3, but I must warn you - don't go into it expecting to be amazed by its platforming.  The platforming alone is pretty average, and is not the selling point of the game.  Go into it expecting an excellent and easy to use drop-in/drop-out multiplayer system, with a wealth of awesome, user made levels for you and your friends to access.  The game is really all about playing with friends and just having a good time. 

Playing with a friend takes no more effort than sending a quick invite on PSN or simply turning on a second controller (they automatically appear in your pod, instantaneously!), and user made levels are streamed ala YouTube, so it's only a few buttons taps from there before you're playing one of the 2.5 million custom levels available.  And friends can join you at literally anytime - while browsing the "menu", which is actually 3D and fully interactive, while playing a level, and so on.

And of course, there's the incredibly robust editor, for those more inclined to create levels than just play them.

I have played this game far more than any other game this generation, and I've spent almost all of my time playing with whoever's at my place or online, going from 5-star level to 5-star level, slapping each other up and in general just screwing around.  It's loads of fun.

And if you happen to be lacking in friends to play with, just hit me up!  I'm playing alllll the time, and will gladly help any noob track down all the items in he story mode, for example.  I've only done it 4-5 times already.  xD

So yeah, it's awesome.  And any fan of Nintendo should theoretically be all over a game like this, given its style and emphasis on sheer fun. 

Yet for some reason some aren't.  Honestly, I find that of the large portion of people that weren't very impressed by the title, almost all of them went into it with the view that its a singleplayer platformer with a level editor tacked on.  "The platforming wasn't that great, and I don't like making levels," they'd say.  Talk about missing the point.

Since you are in a bit similar situation to me (as a pc gamer i'm not interested in fpses on ps3) I'd suggest:

Valkyria Chronicles - this game is briliant in the way it revolutionizes sRPG/strategy genre. Only warning is if you are anime hater you won't be happy with story and background.

Wipeout HD - this is really awesome twitch racer with great visuals and amazing music and is bacilly full game release with psn game price.

Folklore - this is unique action title with great story and very interesting settings (i suggest you try demo from PSN), also probably game with best ever created sisaxis usage for ps3.

Super Stardust HD - ages old classic but looks awesomely in 1080p glory and greatly captures the arcade feeling of orginal.

Heavenly Sword - slasher with great story and probably most badass crazy villains ever created. Also as a Wii gamer you might find those sisaxis controlled sequences very interesting. A bit short so don't pay more than 20$ for it.

Flower- very interesting "game" great to relax and watch some beatifull visuals.

Also check Deamon's Souls - i can't tell you much since i haven't bought it yet but it has a lot of praise going around.

For shit and gigles if you find one for 5$ or less pick up a copy of Lair - game isn't even average but it's interesting case to watch how developers envisioned usage of sisaxis controlls in early ps3 games.

As for controler - get one Dual Shock 3 so you have at least one controler with playstation button, and get converters for ps2 pads for gaming with friends

I'd also stay away from Infamous - this game has a lot of hype going but in the end is just another boring sandbox - so you better check demo. And ditto for Fat Princess - one of the biggest dissapointments i have had with PSN games.

double post

I thought I was going to be the first to mention the rare gem Folklore but I see Zlejedi beat me to it. Otherwise I don't have any games to add to the other suggestions.

Seems to me that as PS3 will be your number 3 console (i.e. the one you play the least) then initially you'll probably want to limit yourself to only a few games that give you experiences unlike what you'll find on Wii or 360. That being the case there are 2 which LEAP to mind immediately:

Valkyria Chronicles

Flower

To a lesser extent there's Demon's Souls. While being a fantastic game, it's still an action RPG at it's core so the experiences are a little closer to what you can find in other action RPGs. Still if you want to get a 3rd game right out of the gate then this is the one.

I agree with you, forget about the FPS's. 360 has all you need there. Though I'd make a plug for MAG in addition to what's already been mentioned. I don't own it, but it's my nephew's most favourite game, he plays it A LOT! His previous FPS experience prior to buying PS3 was all on PC. Personally I don't really dig FPS.

The Uncharted series is fun for the story, great voice acting and brilliant use of in-game dialogue. But it's gameplay is a mix between relatively straightforward platfoming, and fairly standard cover based TPS action. They blend well together for a satisfying experience, but these games don't offer an experience that's unlike anything you can get elsewhere. Though the visuals on Uncharted 2 are spectacular, and on Uncharted 1 the visuals are impressive. These games should be on your list of must gets if you find PS3 usurping 360 as your number 2 most played console. But if PS3 stays in 3rd place for you then it may forever remain on your B list.

Others that are must haves if you find yourself gravitating more towards PS3 over time are: LBP (and I'm sure LBP2 will be something truly special); Infamous; ModNation Racers; you might want to look into Move eventually, though I expect the Wii will keep you more than happy with motion controls for the most part; Ratchet and Clank Series (if you played on PS2 then you really should continue with the series, and Ratchet and Clank: All 4 One looks like it will be a blast and a great new direction for the series gameplay-wise.

God of War III should be a no-brainer if you liked GoW I & II.

All of the games mentioned are great games; but you've got to start somewhere and you have 3 consoles to share your time between.

There are also a ton of cool PSN games, PSN Minis and PSone classics. If you're looking for fairly cheap gaming then you could forget the big brother (Disc based) games and just go PSN all the way. If you decide to go down that track then you could look at signing up for PSN and get really good value for money through the free games and discounted games you get from that service. The only reason I'm not on PSN is because I'd end up playing far too much and the rest of my life would suffer because of it; and worse yet my kids would end up playing far too much.

God of War III -

Uncharted 2 

MGS4 (only if you liked the other ones)

Infamous

Killzone 2, Resistance Fall of Man or Resistance 2

Ratchet and Clank A Crack in Time 

uncharted 2 and oh you dont need the first one to play it, since they tell you the only cross overs which is very simple 

the old guy from the last one and the report but its easy to get in and its a joy of a ride 

Dude God of War 3 , it might be the best game I have ever played. You can also buy inFamous, KillZone or Uncharted.

If you want something unique and good, try Heavy Rain and Flower.