Congratulations on owning one of the greatest gaming systems of all time...aside from the SNES.
The big thing to keep in mind with the DS is that there are tons of third party titles that are just as good, if not better, than the Nintendo games, so don't be afraid to open up and try some new titles that may not be "familiar" to you. The DS is also a region-free device, meaning you can buy and play DS games that were released anywhere in the world. Most people already mentioned all the top games, so I'll give a couple short reviews:
Elite Beat Agents is a MUST, even if you aren't a huge fan of the soundtrack. The gameplay (a touch screen version of 'DDR' if you will) truely outshines the music in every way, and as you play you start forgetting how much you hate artists like Ashley Simpson and Avril Lavigne (well, maybe you enjoy them, but I don't). If for some reason you can't get past the music, you can purchase the Japanese titles that this game originated from (titled Osu! Tatakae! Ouendan!) which features a J-Pop/J-Rock soundtrack, obviously.
Phoenix Wright Ace Attorney/Phoenix Wright Ace Attorney: Justice for All - Phoenix Wright has been an ongoing series in Japan, and luckily it is now being released in the U.S. So far only two of the three titles (soon to be four) have been released in the U.S., but the third is on its way soon. The game is heavily text based, but with a lot of interactivity. To put it simply, it's a detective/lawyer game. You look for clues and evidence that would prove your client is not guilty of a crime they've been accused of. It may sound boring on paper, but the stories and gameplay are surprisingly really great.
Trauma Center: Under the Knife - You play the role of a doctor and use the touch screen to do everything from removing simple throat polyps to removing fictional viruses planted by a terrorist organization. Tons of fun, but gets difficult towards the end.
Pokemon Diamond/Pearl - Probably the most popular titles right now on the DS. If you've played Pokemon before then you'll know what this is. It has some nice graphical updates and a useful global wi-fi trading system, but otherwise the gameplay hasn't changed much.
Lunar Knights - Created by the person that made the Metal Gear Solid series. Great action/RPG with gameplay that's been compared to the top-down Zelda games. The only downside is that all the action takes play in "dungeons" only...the rest of the story is given using still-art/text and cut scenes (which still look really beautiful on the DS)
Bleach DS/Bleach DS 2 - These games are only available in Japanese and you have to hunt it down online to find it, but you can play it on any DS. With a little help of some online FAQs, the game is very easy to figure out, even with knowing zero Japanese. It's a fantastic fighting game comparable to dare I say, Street Fighter?
Castlevania: Dawn of Sorrow/Castlevania: Portrait of Ruin - Two exclusive Castlevania titles for the DS. Definitely some of the best games on this system. Long and addictive action-adventure-RPG.
Animal Crossing: Wild World - If you're a fan of life simulation games like The Sims, you'll probably enjoy this slightly simplified version where you play a boy/girl that moves into a town inhabited by animals. You earn money by doing simple tasks and you gradually use the money to make your house bigger and buy items for the house or clothing to customize your character. It's a hit or miss title, and it does get boring eventually, but I always find myself coming back to it. Tons of replay value and very addictive.
These are all games that I own and enjoy. The biggest problem with the DS is that there are so many great titles that you'll have a hard time affording to buy them all or play them all for that matter (I never had this problem with my PSP!
)
As far as screen protectors, I wouldn't worry about them. I had some on my DS originally, but I took them off at one point and never looked back. Believe it or not, the screens are very scratch resistant, even with heavy use. Just keep a soft cloth close (the ones for cleaning eyeglasses are great) and you can just wipe the "scratches" away.
For cases...I've been using my PSP soft case ironically. I'm thinking of purchasing this case though:
http://www.gamestop.com/product.asp?product_id=802602
It seems to have gotten good reviews and it looks like a good case overall...plus it's cheap, which you can't go wrong with.
If you have any more questions about the DS, let me know...I'm kind of a DS addict, incase you can't tell.
