The Microsoft MPEG4 codec is a very old Microsoft implementation of MPEG-4 Part 2 Simple Profile. Back in 1998, Microsoft came up with three versions, namly Microsoft MPEG4 v1, v2, v3. All of these are now considered to be obsolete, low quality and not ISO/IEC compliant. These means that if you capture your video in this format, you might not be able to play it back on your hardware devices i.e. your MPEG-4 capable DVD Player
The DivX codec originally started off with DivX ;-) 3.11, which is basically a hack of M$ MPEG-4 codec v3. DivX is now currently owned by DivX, Inc. DivX 6.4 is their lastest version, and development all these years has resulted DivX in much improved quality and speed as compared to Microsoft's implementation. The DivX codec is now MPEG-4 Part2 Advanced Simple Profile compliant, and you will be able to play it on many MPEG-4 capable DVD players available now. The only drawback is that DivX is proprietary and not free. There is a 15-day trial available, thereafter, the DivX codec will revert itself into a free version with limited feature and tools.
There is a free and open source alternative, XviD. Its quality and speed are comparable, and in most cases, exceed DivX in serveral codec shootouts, eg. http://www.doom9.org/codec-comparisons.htm . XviD is ISO/IEC compliant, and you will be able to play it on many MPEG-4 capable DVD players. I personally recomend that you should try XviD instead of the previous two. There is a large community of XviD users that can provide you help if you need any, http://forum.doom9.org/forumdisplay.php?f=52 . The lastest version, XviD 1.1.2, can be downloaded from serveral places, eg. http://www.koepi.org/xvid.shtml .
Have fun :)