As a basic cart which excels at playing games the
Acekard 2i is very popular, it has great compatibility and is the cheapest realistic DSi cart. The thing to remember is the Acekard 2i requires a firmware update to be compatible with DSi FirmWare 1.4, which is the firmware any new DSi or DSi XL will have. The firmware update can only be performed using a DS Lite or DS Phat. If you don't have one of them to update it, you can purchase it from somewhere like
ShopTemp and they will update it before shipping for an additional $1 (select the premium update option when you add it to the basket) It's the most popular DSi cart at the moment.
The
DSTWO has many additional features such as Real time save, Real time cheats, Real time guide, GBA Emulation (it has an additional built in processor for this). It also has DivX and SNES emulation in the works. They are due to release the Software Development Kit, which will likely lead to some improved homebrew/ emulators. They downside is that it's $20 more expensive, and it's built in processor reduces battery life slightly. Given time it should easily be the best cart. Unlike the Acekard, it's firmware can be updated on any DSi.
If you want something middle of the road, you have the EZ-Flash Vi or the DSONEi. They have Real Time Save like the DSTWO, but lack the GBA emulation, DIVX etc,
Whatever you do, do not buy any R4i carts. They are all clones, and have very poor support/ compatibility.