When I run lspci command i get this:

00:00.0 Host bridge: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor DRAM Controller (rev 09)
00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor PCI Express Root Port (rev 09)
00:02.0 Display controller: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor Graphics Controller (rev 09)
00:16.0 Communication controller: Intel Corporation 6 Series/C200 Series Chipset Family MEI Controller #1 (rev 04)
00:1a.0 USB controller: Intel Corporation 6 Series/C200 Series Chipset Family USB Enhanced Host Controller #2 (rev 05)
00:1b.0 Audio device: Intel Corporation 6 Series/C200 Series Chipset Family High Definition Audio Controller (rev 05)
00:1c.0 PCI bridge: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 1 (rev b5)
00:1c.1 PCI bridge: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 2 (rev b5)
00:1c.2 PCI bridge: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 3 (rev b5)
00:1d.0 USB controller: Intel Corporation 6 Series/C200 Series Chipset Family USB Enhanced Host Controller #1 (rev 05)
00:1f.0 ISA bridge: Intel Corporation H61 Express Chipset Family LPC Controller (rev 05)
00:1f.2 SATA controller: Intel Corporation 6 Series/C200 Series Chipset Family SATA AHCI Controller (rev 05)
00:1f.3 SMBus: Intel Corporation 6 Series/C200 Series Chipset Family SMBus Controller (rev 05)
01:00.0 VGA compatible controller: NVIDIA Corporation GK104 [GeForce GTX 660 OEM] (rev a1)
01:00.1 Audio device: NVIDIA Corporation GK104 HDMI Audio Controller (rev a1)
02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 06)
03:00.0 USB controller: Renesas Technology Corp. uPD720202 USB 3.0 Host Controller (rev 02)
04:00.0 Network controller: Qualcomm Atheros AR9485 Wireless Network Adapter (rev 01)


Now I am no expert at Linux drivers and how their graphics stuff works, but I know in Windows I could display my integrated Intel graphics via Device Manager as to ensure my computer was pushing everything thru my Nvidia GTX 660 card.

So my questions is, why is my Display Controller Intel when I have an Nvidia card? Or is this just the way it is supposed to be, because I have been running a couple of games that have nice graphics at maxed settings and I doubt the Intel could keep up with that...but I just can't figure out why it says Intel under Display Controller.

Any feedback would be helpful, and I tried finding the answer to this but I am thinking it is such a simple answer that no one has ever asked before...


Question: Modern design - What's that?
Answer: From my understanding of what you are asking it is very subjective to quantify a design as " modern". However many website design maybe considered "modern" because of their presentation, look and feel, inclusions of interactive graphics (html 5, JavaScript, flash) and beautiful illustrations on the website. Some may consider your website old because it visually looks like ... well old website :( (pre-drupal,wordpress even pre-flash)
Your website looks very plainly a very simplistic design (which is good thing) but is not appealing visually. You should try and change your layout, integrate your logo better into your site and also try to add an animated banner. Also the "thanks a lot" is a little old fashioned.
You really don't have to look very hard to find cool and inspirational designs on the internet :)  

Most of today's websites which maybe considered modern are made using Drupal, Wordpress, Joomla or another CMS (but these 3 are very well known. open source and you can download them for free)  

Here's the basic layout for Drupal and what you can do:
  


For some cool buttons see here  
For a menu bar that moves with the page scroll you can see this  
For a drop down menu you can see this  
You can make a slider/slideshow on your own or use software for it like SlideShowPro or a free one - WOW Slider.You can do all sorts of things with this - make it scrollable and in many cases its a good idea to link it to your menu bar. (See here for some inspiration)  
For smooth scrolling see this    


The rest really is upto you. Make good use of the Triptych part ... it can make your site go from cool to awesome (again see smooth scrolling - this is extremely handy). Use AJAX to make your site more dynamic (because modern designs won't just relate to the visual appeal of your website but also the interaction of your site with the viewer) (jQuery makes life simple here).  


For some cool ideas of what this or a similar layout scheme can be tailored into see here.  
See this for some more inspiration     


Here's the thing mate: You can skip all of this and just do your own thing. How you design essentially comes from you. Its your way of looking at things. Wordpress, Joomla and Drupal are used extensively in modern websites - from big corporate names to everyday users. Now to go back to your title question of "modern" design - pardon me here, but I don't know what is the purpose of your website, your deadlines or client - But the latest in web design is HTML5. Check out the Chrome Experiments, which really are making these designs look outdated, and some cool sites built using HTML5 and JavaScript.