When using the onboard video option in your silent computer, your graphics capability is determined by the processor you choose, and the video ports are determined by your motherboard's onboard headers. Here is a basic rundown of the onboard graphics capabilities of the different series of Intel CPUs.
Intel Celeron Processors: Intel Celeron Processors feature the generic Intel HD graphics, which is primarily made for basic uses such as text editing, basic video, and general office or web-work. Intel HD graphics arent made for games or HD Video.
Intel Pentium Processors: The Intel Pentium Processors feature the same generic Intel HD graphics as the Celeron family. Not reccomended for HD video or Games.
Intel Core i3 Processors: The Intel Core i3 Processors feature the Intel HD 4400 series Graphics, which are much better than the generic Intel HD graphics found in the Celeron and Pentium familys, and are capable of playing back HD video, as well as some very basic games.
Intel Core i5 Processors: Intel Core i5 Processors feature the Intel HD 4600 series Graphics are quite a bit more powerful than the 4400 series, and can easily handle HD video playback, as well as some moderate gaming.
Intel Core i7 Processors: The current Core i7 Processors also feature the Intel HD 4600 series Graphics, but are faster CPUs in general, so they tend to handle gaming much better than the i5 series processors. Serious gamers will defintiely still want to go for a standard add-in vdieo card in lieu of using onboard graphics.
If you are interested in some benchmarks, PassMark has a good direct comparison between the HD 4400 and HD 4600 Series Intel graphics that can be found here.