I have a Asus X99-E WS motherboard (LGA 2011 v3 slot) and it doesn't come with any video ports. Is it still possible to use the video capabilities of the Intel CPU or will I need to purchase a video card? If a video card is required, what is recommended for good video quality with an HDMI port (24p movies, etc.)?
LGA 2011 processors typically don't have built in graphics like lesser models. That said nearly any modern card will quite handle video at up to 60hz at common resolutions. 4K might be tricky, but at worst you need a mid range card.
That said, I disagree on the suggestion of a super cheap, old card.
There's a few reasons. The specific nvidia line that mark mentioned on his answer's a bit problematic, and has a high failure rate. Its also roughly 7-8 years old, and its a little like putting a bike tyre on a bugatti veyron.
Depending on your needs a gforce 700 or 900 series, preferably midrange (a 960 upwards, but I paired my 'regular' core i7 3rd generation with a top of the line card, and its really good). If you have really have basic needs (and what you do does!) go with a lower end card, but preferably within the current or previous generations. The oldest I'd go is the 600 series.
What should you be looking for? HDMI's what you'd connect a TV with, and is standard. DP is the standard for computer monitors. Make sure your card has both.
Why get a better card over an old one?
They often have better gpgpu capabilities and video playback acceleration. You can often use your GPU to play back video. You also are more likely to have warranty coverage.
You may be able to use the video-transcoding capabilities of the Intel integrated graphics, but with no video port on the board, you won't be able to use it to drive a monitor.
If all you need out of a video card is the ability to play movies and show desktop graphics (ie. no gaming), any low-end card will do. $30 will get you something like the XFX One Radeon HD 5450 ON-XFX1-PLS2 or the EVGA GeForce 8400 GS 01G-P3-1303-KR.