Do I need a video card?
With older systems, the 'onboard' graphics was a distinct chip on the motherboard. With modern intel systems, from sandy bridge onwards, its part of the CPU. The chipset that the video adaptor was part of has been merged into the CPU proper.
The mainstream processors the z97 is designed for have GPUs built in. The server chips do not, and the onboard graphics outs simply would not work. You'd want to consider a comparable mainstream processor to use the onboard graphics, or to use pretty much any PCIe graphics card.
So in this specific case, you do need a seperate graphics card, and your onboard ports will do nothing at all.
More generally, if an intel processor from sandy bridge generation or later has integrated video, its on chip. All xeons, and some mainstream processors would not have the graphics core, and any on board video wouldn't work.
A good way is to check the intel ARK page for the processor and check for "CPU graphics* as you did, and assume any board with 'none' will not have the on board ports functional.
In addition some boards don't have graphics out (which would be obvious), or let you use processor graphics and discrete graphics at once (The SB era P series boards for example). Any board that supports lucid logix should let you run both at once
With AMD processors, in general A-Series processors always have onboard video, FX series and opterons don't. I don't have direct experience with these, but this seems to be the case off wikipedia.
Generally server boards have low end graphics chips as opposed to on processor graphics, since they can safely assume you have no GPU, nor the desire to install one.
You don't need a display card for this. The motherboard in question has a GPU, and it has VGA, HDMI and DVI outputs directly on the board.
The technician you talked to obviously had no idea, or was trying to upsell you the display card.
Don't expect to be gaming from this setup, but desktop work and videos should work just fine. You can always add a display card if you find you need one for heavier graphics. Be aware that the maximum resolution on DVI is 1920x1200, but if you can use HDMI it can go up to a higher resolution.
The specs for the board says:
Integrated Graphics Processor:
1 x D-Sub port, supporting a maximum resolution of 1920x1200@60Hz
1 x DVI-D port, supporting a maximum resolution of 1920x1200@60Hz
* The DVI-D port does not support D-Sub connection by adapter.
1 x HDMI port, supporting a maximum resolution of 4096x2160@24Hz or 2560x1600@60Hz
* Support for HDMI 1.4a version. Support for up to 3 displays at the same time Maximum shared memory of 512MB