I would go for a desktop every time unless you need complete portability. A desktop,and its peripherals, can be more easily upgraded/repaired/ than a laptop/tablet and is much more robust if having a lot of use. If you are a touch-typist then having a proper key board, mouse and monitor is much better.
Personally I would not want a touchscreen on my main desktop PC for the main reason that it would be very tiring reaching up to operate it and not very comfortable if you have a large screen that is quite close to you. You can of course opt to have a mouse and a regular keyboard but this defeats the object - I think touchscreens are best reserved for tablets.
If you have to plug in peripherals to whatever you buy then portability is impaired anyway.
Just a question - why would you want to watch tv and use your laptop at the same time? Maybe you need more than one PC?