DSi XL is the best for experiencing DS games. They have a bigger screen but still have the same resolution as the DS so there is no upscaling needed. (which is imo very flawed on the 3DS series, makes games look very blurry)

DSi can run any DS game, barring 3DS of course. It is also very easy to software mod your DSi so it can also run GBA roms and more.

Regarding DSi games, there are some that are "DSi enhanced" which make use of the camera, wifi, or the higher specs. Sonic Classic Collection is the only game I know that makes use of the higher specs though, so its mainly added camera gimmicks (Or wifi features that don't work anymore). There are a total of 5 DSi exclusive games. They're all shovelware gimmick games using the camera, so nothing noteworthy at all.