Should I buy it used or new?
New means the safety of a warranty for a certain amount of time, old *might* (depending on who owned it before you) mean there could be some downloaded games on it already, it could also mean the console could be worn, have scratches, etc, so if you buy an old, demand to inspect it in the store so you know what you're buying (I once bought an old Gamecube, the console itself was good, but the controller was so worn it was next to impossible to play with it - which was a shame since it was the controller I was looking to get, because I wanted to use it to play Gamecube and N64 games on my wii). You need to decide what is more important to you and also what fits your budget.
Should I get any accessories for it?
I'd definitely get some kind of casing around it, not only can they be decorative, but they also help protect the console. I keep mine in my purse, so it comes with me wherever I go, so I've doubled up on protection. I have the Zelda OoT crystal casing on the console itself:
Amazon.com: Nintendo 3DS Zelda Crystal Armor Case: Video Games
And when I'm not playing it, I keep my 3DS in this wallet (I chose that particular one because it's compact and I already have a case for all my games, so I didn't need one that accomendated for more games and accessories):
Mad Catz Officially Licensed 3DS Microsuede Wallet - Blue
Where should I buy a 3ds?
Figure out which retailers (online or off) you find more trustworthy that offers the best prices. I bought mine at HMV at Heathrow airport, because I got it much cheaper and tax-free, due to the fact I was flying abroad, plus I got it right away, lol. But you need to decide what suits you more.
What games should i buy for my 3ds?
The only 3DS games I have right now are the Occarina of Time 3DS and Mario 3DS, both of which I would greatly recommend. The 3DS also have the eShop where you can buy a lot of games, plus you can play regular DS games on it (however if the games require certain accessories, make sure the accessories are appropriate for the 3DS - I once bougt the Guitar Hero on DS, only to discover the guitar accessory didn't fit the 3DS - luckily both my nieces had DS-es that could use it, so the game ended up being used by someone, at least, lol)
Is a 3ds worth buying?
For me it was, without a doubt. However I never owned a regular DS, so it all depends on whether you already have a DS and if you find the added features on the 3DS truly worth it compared to the DS you already have. If you however don't already have a DS, then the 3DS is a really great buy, because it has backwards compability so you can not only enjoy all the 3DS titles, but also all other DS titles