Nothing prohibits you from using a TV tuner card with Windows Vista Home Basic..But you have to ensure that the driver software,the PVR software and whatever software that comes with the card are Vista compatible.You may also perhaps need to install a Video decoder.(present in Power DVD)
Yes, Windows Vista Home premium comes with Media center program integrated into it and also Windows Video decoder..When used with vista compatible TV tuner card, the Media center program automatically kicks in the built-in PVR program and you can pause, rewind live TV, and use it as a PVR.No need to install the manufacturer provided PVR software.You also get many other media center facilities.If you can get the Mediacenter specific IR Receiver and infrared remote you can control all the media center functions with the remote. For more about the media center search the Microsoft site. Effectively Vista Home premium replaces the Windows XP Media center edition 2005.